Model Predictive Static Programming: A Computationally Efficient Technique For Suboptimal Control Design

Combining the philosophies of nonlinear model predictive control and approximate dynamic programming, a new suboptimal control design technique is presented in this paper, named as model predictive static programming (MPSP), which is applicable for finite-horizon nonlinear problems with terminal constraints. This technique is computationally efficient, and hence, can possibly be implemented online. The effectiveness of the proposed method is demonstrated by designing an ascent phase guidance scheme for a ballistic missile propelled by solid motors. A comparison study with a conventional gradient method shows that the MPSP solution is quite close to the optimal solution.

A near Optimal Cane Rail Scheduler under Limited and Unlimited Capacity Constraints

Australia is the world’s third largest exporter of raw sugar after Brazil and Thailand, with around $2.0 billion in export earnings. Transport systems play a vital role in the raw sugar production process by transporting the sugarcane crop between farms and mills. In 2013, 87 per cent of sugarcane was transported to mills by cane railway. The total cost of sugarcane transport operations is very high. Over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. A cane railway network mainly involves single track sections and multiple track sections used as passing loops or sidings. The cane railway system performs two main tasks: delivering empty bins from the mill to the sidings for filling by harvesters; and collecting the full bins of cane from the sidings and transporting them to the mill. A typical locomotive run involves an empty train (locomotive and empty bins) departing from the mill, traversing some track sections and delivering bins at specified sidings. The locomotive then, returns to the mill, traversing the same track sections in reverse order, collecting full bins along the way. In practice, a single track section can be occupied by only one train at a time, while more than one train can use a passing loop (parallel sections) at a time. The sugarcane transport system is a complex system that includes a large number of variables and elements. These elements work together to achieve the main system objectives of satisfying both mill and harvester requirements and improving the efficiency of the system in terms of low overall costs. These costs include delay, congestion, operating and maintenance costs. An effective cane rail scheduler will assist the traffic officers at the mill to keep a continuous supply of empty bins to harvesters and full bins to the mill with a minimum cost. This paper addresses the cane rail scheduling problem under rail siding capacity constraints where limited and unlimited siding capacities were investigated with different numbers of trains and different train speeds. The total operating time as a function of the number of trains, train shifts and a limited number of cane bins have been calculated for the different siding capacity constraints. A mathematical programming approach has been used to develop a new scheduler for the cane rail transport system under limited and unlimited constraints. The new scheduler aims to reduce the total costs associated with the cane rail transport system that are a function of the number of bins and total operating costs. The proposed metaheuristic techniques have been used to find near optimal solutions of the cane rail scheduling problem and provide different possible solutions to avoid being stuck in local optima. A numerical investigation and sensitivity analysis study is presented to demonstrate that high quality solutions for large scale cane rail scheduling problems are obtainable in a reasonable time. Keywords: Cane railway, mathematical programming, capacity, metaheuristics

Optimal dynamic inversion-based semi-active control of benchmark bridge using MR dampers

A new two-stage state feedback control design approach has been developed to monitor the voltage supplied to magnetorheological (MR) dampers for semi-active vibration control of the benchmark highway bridge. The first stage contains a primary controller, which provides the force required to obtain a desired closed-loop response of the system. In the second stage, an optimal dynamic inversion (ODI) approach has been developed to obtain the amount of voltage to be supplied to each of the MR dampers such that it provides the required force prescribed by the primary controller. ODI is formulated by optimization with dynamic inversion, such that an optimal voltage is supplied to each damper in a set. The proposed control design has been simulated for both phase-I and phase-II study of the recently developed benchmark highway bridge problem. The efficiency of the proposed controller is analyzed in terms of the performance indices defined in the benchmark problem definition. Simulation results demonstrate that the proposed approach generally reduces peak response quantities over those obtained from the sample semi-active controller, although some response quantities have been seen to be increasing. Overall, the proposed control approach is quite competitive as compared with the sample semi-active control approach.

Essays on socially optimal phosphorus policies in crop production

Phosphorus is a nutrient needed in crop production. While boosting crop yields it may also accelerate eutrophication in the surface waters receiving the phosphorus runoff. The privately optimal level of phosphorus use is determined by the input and output prices, and the crop response to phosphorus. Socially optimal use also takes into account the impact of phosphorus runoff on water quality. Increased eutrophication decreases the economic value of surface waters by Deteriorating fish stocks, curtailing the potential for recreational activities and by increasing the probabilities of mass algae blooms. In this dissertation, the optimal use of phosphorus is modelled as a dynamic optimization problem. The potentially plant available phosphorus accumulated in soil is treated as a dynamic state variable, the control variable being the annual phosphorus fertilization. For crop response to phosphorus, the state variable is more important than the annual fertilization. The level of this state variable is also a key determinant of the runoff of dissolved, reactive phosphorus. Also the loss of particulate phosphorus due to erosion is considered in the thesis, as well as its mitigation by constructing vegetative buffers. The dynamic model is applied for crop production on clay soils. At the steady state, the analysis focuses on the effects of prices, damage parameterization, discount rate and soil phosphorus carryover capacity on optimal steady state phosphorus use. The economic instruments needed to sustain the social optimum are also analyzed. According to the results the economic incentives should be conditioned on soil phosphorus values directly, rather than on annual phosphorus applications. The results also emphasize the substantial effects the differences in varying discount rates of the farmer and the social planner have on optimal instruments. The thesis analyzes the optimal soil phosphorus paths from its alternative initial levels. It also examines how erosion susceptibility of a parcel affects these optimal paths. The results underline the significance of the prevailing soil phosphorus status on optimal fertilization levels. With very high initial soil phosphorus levels, both the privately and socially optimal phosphorus application levels are close to zero as the state variable is driven towards its steady state. The soil phosphorus processes are slow. Therefore, depleting high phosphorus soils may take decades. The thesis also presents a methodologically interesting phenomenon in problems of maximizing the flow of discounted payoffs. When both the benefits and damages are related to the same state variable, the steady state solution may have an interesting property, under very general conditions: The tail of the payoffs of the privately optimal path as well as the steady state may provide a higher social welfare than the respective tail of the socially optimal path. The result is formalized and an applied to the created framework of optimal phosphorus use.

Improved chemical control of Conyza bonariensis in wheat limits problems in the following fallow

Conyza bonariensis is a major weed infesting zero-tilled cropping systems in subtropical Australia, particularly in wheat and winter fallows. Uncontrolled C.bonariensis survives to become a problem weed in the following crops or fallows. As no herbicide has been registered for C.bonariensis in wheat, the effectiveness of 11 herbicides, currently registered for other broad-leaved weeds in wheat, was evaluated in two pot and two field experiments. As previous research showed that the age of C.bonariensis, and to a lesser extent, the soil moisture at spraying affected herbicide efficacy, these factors also were investigated. The efficacy of the majority of herbicide treatments was reduced when large rosettes (5-15cm diameter) were treated, compared with small rosettes (<5cm diameter). However, for the majority of herbicide treatments, the soil moisture did not affect the herbicide efficacy in the pot experiments. In the field, a delay in herbicide treatment of 2 weeks reduced the herbicide efficacy consistently across herbicide treatments, which was related to weed age but not to soil moisture differences. Across all the experiments, four herbicides controlled C.bonariensis in wheat consistently (83-100%): 2,4-D; aminopyralid + fluroxypyr; picloram + MCPA + metsulfuron; and picloram + high rates of 2,4-D. Thus, this problem weed can be effectively and consistently controlled in wheat, particularly when small rosettes are treated, and therefore C.bonariensis will have a less adverse impact on the following fallow or crop.

Weeds of Direct-Seeded Rice in Asia: Problems and Opportunities

Rice production symbolizes the single largest land use for food production on the Earth. The significance of this cereal as a source of energy and income seems overwhelming for millions of people in Asia, representing 90% of global rice production and consumption. Estimates indicate that the burgeoning population will need 25% more rice by 2025 than today's consumption. As the demand for rice is increasing, its production in Asia is threatened by a dwindling natural resource base, socioeconomic limitations, and uncertainty of climatic optima. Transplanting in puddled soil with continuous flooding is a common method of rice crop establishment in Asia. There is a dire need to look for rice production technologies that not only cope with existing limitations of transplanted rice but also are viable, economical, and secure for future food demand.Direct seeding of rice has evolved as a potential alternative to the current detrimental practice of puddling and nursery transplanting. The associated benefits include higher water productivity, less labor and energy inputs, less methane emissions, elimination of time and edaphic conflicts in the rice-wheat cropping system, and early crop maturity. Realization of the yield potential and sustainability of this resource-conserving rice production technique lies primarily in sustainable weed management, since weeds have been recognized as the single largest biological constraint in direct-seeded rice (DSR). Weed competition can reduce DSR yield by 30-80% and even complete crop failure can occur under specific conditions. Understanding the dynamics and outcomes of weed-crop competition in DSR requires sound knowledge of weed ecology, besides production factors that influence both rice and weeds, as well as their association. Successful adoption of direct seeding at the farmers' level in Asia will largely depend on whether farmers can control weeds and prevent shifts in weed populations from intractable weeds to more difficult-to-control weeds as a consequence of direct seeding. Sustainable weed management in DSR comprises all the factors that give DSR a competitive edge over weeds regarding acquisition and use of growth resources. This warrants the need to integrate various cultural practices with weed control measures in order to broaden the spectrum of activity against weed flora. A weed control program focusing entirely on herbicides is no longer ecologically sound, economically feasible, and effective against diverse weed flora and may result in the evolution of herbicide-resistant weed biotypes. Rotation of herbicides with contrasting modes of action in conjunction with cultural measures such as the use of weed-competitive rice cultivars, sowing time, stale seedbed technique, seeding rate, crop row spacing, fertilizer and water inputs and their application method/timing, and manual and mechanical hoeing can prove more effective and need to be optimized keeping in view the type and intensity of weed infestation. This chapter tries to unravel the dynamics of weed-crop competition in DSR. Technological issues, limitations associated with DSR, and opportunities to combat the weed menace are also discussed as a pragmatic approach for sustainable DSR production. A realistic approach to secure yield targets against weed competition will combine the abovementioned strategies and tactics in a coordinated manner. This chapter further suggests the need of multifaceted and interdisciplinary research into ecologically based weed management, as DSR seems inevitable in the near future.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

Jointly optimal power control and routing for a single cell, dense, ad hoc wireless network

We consider a dense, ad hoc wireless network confined to a small region, such that direct communication is possible between any pair of nodes. The physical communication model is that a receiver decodes the signal from a single transmitter, while treating all other signals as interference. Data packets are sent between source-destination pairs by multihop relaying. We assume that nodes self-organise into a multihop network such that all hops are of length d meters, where d is a design parameter. There is a contention based multiaccess scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, we seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d, subject to an average power constraint. We first argue that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc network (described above) as a single cell, we study the optimal hop length and power control that maximizes the transport capacity for a given network power constraint. More specifically, for a fading channel and for a fixed transmission time strategy (akin to the IEEE 802.11 TXOP), we find that there exists an intrinsic aggregate bit rate (Theta(opt) bits per second, depending on the contention mechanism and the channel fading characteristics) carried by the network, when operating at the optimal hop length and power control. The optimal transport capacity is of the form d(opt)((P) over bar (t)) x Theta(opt) with d(opt) scaling as (P) over bar (1/eta)(t), where (P) over bar (t) is the available time average transmit power and eta is the path loss exponent. Under certain conditions on the fading distribution, we then provide a simple characterisation of the optimal operating point.

Discrete parameter simulation optimization algorithms with applications to admission control with dependent service times

We propose certain discrete parameter variants of well known simulation optimization algorithms. Two of these algorithms are based on the smoothed functional (SF) technique while two others are based on the simultaneous perturbation stochastic approximation (SPSA) method. They differ from each other in the way perturbations are obtained and also the manner in which projections and parameter updates are performed. All our algorithms use two simulations and two-timescale stochastic approximation. As an application setting, we consider the important problem of admission control of packets in communication networks under dependent service times. We consider a discrete time slotted queueing model of the system and consider two different scenarios - one where the service times have a dependence on the system state and the other where they depend on the number of arrivals in a time slot. Under our settings, the simulated objective function appears ill-behaved with multiple local minima and a unique global minimum characterized by a sharp dip in the objective function in a small region of the parameter space. We compare the performance of our algorithms on these settings and observe that the two SF algorithms show the best results overall. In fact, in many cases studied, SF algorithms converge to the global minimum.

Experimental Demonstration of H{infty} Control based Active Vibration Suppression in Composite Fin-tip of Aircraft using Optimally Placed Piezoelectric Patch Actuators

The goal of this study is the multi-mode structural vibration control in the composite fin-tip of an aircraft. Structural model of the composite fin-tip with surface bonded piezoelectric actuators is developed using the finite element method. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes accurately. A model order reduction technique is employed for reducing the finite element structural matrices before developing the controller. Particle swarm based evolutionary optimization technique is used for optimal placement of piezoelectric patch actuators and accelerometer sensors to suppress vibration. H{infty} based active vibration controllers are designed directly in the discrete domain and implemented using dSpace® (DS-1005) electronic signal processing boards. Significant vibration suppression in the multiple bending modes of interest is experimentally demonstrated for sinusoidal and band limited white noise forcing functions.

Optimal Nonlinear Control and Estimation for a Reusable Launch Vehicle During Reentry Phase

In this paper a nonlinear optimal controller has been designed for aerodynamic control during the reentry phase of the Reusable Launch Vehicle (RLV). The controller has been designed based on a recently developed technique Optimal Dynamic Inversion (ODI). For full state feedback the controller has required full information about the system states. In this work an Extended Kalman filter (EKF) is developed to estimate the states. The vehicle (RLV) has been has been consider as a nonlinear Six-Degree-Of-Freedom (6-DOF) model. The simulation results shows that EKF gives a very good estimation of the states and it is working well with ODI. The resultant trajectories are very similar to those obtained by perfect state feedback using ODI only.

Uplink Power Control and Base Station Association in Multichannel Cellular Networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Optimal Reservoir Operation for Flood Control Using Folded Dynamic Programming

Folded Dynamic Programming (FDP) is adopted for developing optimalnreservoir operation policies for flood control. It is applied to a case study of Hirakud Reservoir in Mahanadi basin, India with the objective of deriving optimal policy for flood control. The river flows down to Naraj, the head of delta where a major city is located and finally joins the Bay of Bengal. As Hirakud reservoir is on the upstream side of delta area in the basin, it plays an important role in alleviating the severity of the flood for this area. Data of 68 floods such as peaks of inflow hydrograph, peak of outflow from reservoir during each flood, peak of flow hydrograph at Naraj and d/s catchment contribution are utilized. The combinations of 51, 54, 57 thousand cumecs as peak inflow into reservoir and 25.5, 20, 14 thousand cumecs respectively as,peak d/s catchment contribution form the critical combinations for flood situation. It is observed that the combination of 57 thousand cumecs of inflow into reservoir and 14 thousand cumecs for d/s catchment contribution is the most critical among the critical combinations of flow series. The method proposed can be extended to similar situations for deriving reservoir operating policies for flood control.