Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle Using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A I-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Reduced Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and /spl thetas/-D Techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems. First proper orthogonal decomposition based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. Next, a suboptimal controller is designed using the emerging /spl thetas/-D technique for lumped parameter systems. This time domain sub-optimal control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state feedback form. Numerical results for a real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good suboptimal control design technique for distributed parameter systems.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator)

On the optimality of exhaustive service policies in multiclass queueing systems with modulated arrivals and switchovers

Consider a single-server multiclass queueing system with K classes where the individual queues are fed by K-correlated interrupted Poisson streams generated in the states of a K-state stationary modulating Markov chain. The service times for all the classes are drawn independently from the same distribution. There is a setup time (and/or a setup cost) incurred whenever the server switches from one queue to another. It is required to minimize the sum of discounted inventory and setup costs over an infinite horizon. We provide sufficient conditions under which exhaustive service policies are optimal. We then present some simulation results for a two-class queueing system to show that exhaustive, threshold policies outperform non-exhaustive policies.

A Complete Characterization of an Optimal Timer Based Selection Scheme

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.

X-Codes: A Low Complexity Full-Rate High-Diversity Achieving Precoder for TDD MIMO Systems

We consider a time division duplex multiple-input multiple-output (nt × nr MIMO). Using channel state information (CSI) at the transmitter, singular value decomposition (SVD) of the channel matrix is performed. This transforms the MIMO channel into parallel subchannels, but has a low overall diversity order. Hence, we propose X-Codes which achieve a higher diversity order by pairing the subchannels, prior to SVD preceding. In particular, each pair of information symbols is encoded by a fixed 2 × 2 real rotation matrix. X-Codes can be decoded using nr very low complexity two-dimensional real sphere decoders. Error probability analysis for X-Codes enables us to choose the optimal pairing and the optimal rotation angle for each pair. Finally, we show that our new scheme outperforms other low complexity precoding schemes.

Damped Belief Propagation Based Near-Optimal Equalization of Severely Delay-Spread UWB MIMO-ISI Channels

In this paper, we present a belief propagation (BP) based equalizer for ultrawideband (UWB) multiple-input multiple-output (MIMO) inter-symbol interference (ISI) channels characterized by severe delay spreads. We employ a Markov random field (MRF) graphical model of the system on which we carry out message passing. The proposed BP equalizer is shown to perform increasingly closer to optimal performance for increasing number of multipath components (MPC) at a much lesser complexity than that of the optimum equalizer. The proposed equalizer performs close to within 0.25 dB of SISO AWGN performance at 10-3 bit error rate on a severely delay-spread MIMO-ISI channel with 20 equal-energy MPCs. We point out that, although MIMO/UWB systems are characterized by fully/densely connected graphical models, the following two proposed features are instrumental in achieving near-optimal performance for large number of MPCs at low complexities: i) use of pairwise compatibility functions in densely connected MRFs, and ii) use of damping of messages.

Integrated Reservoir Operation Modeling for Irrigation Systems - A Multi-Objective Approach

An integrated reservoir operation model is presented for developing effective operational policies for irrigation water management. In arid and semi-arid climates, owing to dynamic changes in the hydroclimatic conditions within a season, the fixed cropping pattern with conventional operating policies, may have considerable impact on the performance of the irrigation system and may affect the economics of the farming community. For optimal allocation of irrigation water in a season, development of effective mathematical models may guide the water managers in proper decision making and consequently help in reducing the adverse effects of water shortage and crop failure problems. This paper presents a multi-objective integrated reservoir operation model for multi-crop irrigation system. To solve the multi-objective model, a recent swarm intelligence technique, namely elitist-mutated multi-objective particle swarm optimisation (EM-MOPSO) has been used and applied to a case study in India. The method evolves effective strategies for irrigation crop planning and operation policies for a reservoir system, and thereby helps farming community in improving crop benefits and water resource usage in the reservoir command area.

Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

On Optimal Performance in Mobile Ad-Hoc Networks

In this paper we are concerned with finding the maximum throughput that a mobile ad hoc network can support. Even when nodes are stationary, the problem of determining the capacity region has long been known to be NP-hard. Mobility introduces an additional dimension of complexity because nodes now also have to decide when they should initiate route discovery. Since route discovery involves communication and computation overhead, it should not be invoked very often. On the other hand, mobility implies that routes are bound to become stale resulting in sub-optimal performance if routes are not updated. We attempt to gain some understanding of these effects by considering a simple one-dimensional network model. The simplicity of our model allows us to use stochastic dynamic programming (SDP) to find the maximum possible network throughput with ideal routing and medium access control (MAC) scheduling. Using the optimal value as a benchmark, we also propose and evaluate the performance of a simple threshold-based heuristic. Unlike the optimal policy which requires considerable state information, the heuristic is very simple to implement and is not overly sensitive to the threshold value used. We find empirical conditions for our heuristic to be near-optimal as well as network scenarios when our simple heuristic does not perform very well. We provide extensive numerical and simulation results for different parameter settings of our model.

MAX: A Multi Objective Memory Architecture eXploration Framework for Embedded Systems-on-Chip

Today's feature-rich multimedia products require embedded system solution with complex System-on-Chip (SoC) to meet market expectations of high performance at a low cost and lower energy consumption. The memory architecture of the embedded system strongly influences these parameters. Hence the embedded system designer performs a complete memory architecture exploration. This problem is a multi-objective optimization problem and can be tackled as a two-level optimization problem. The outer level explores various memory architecture while the inner level explores placement of data sections (data layout problem) to minimize memory stalls. Further, the designer would be interested in multiple optimal design points to address various market segments. However, tight time-to-market constraints enforces short design cycle time. In this paper we address the multi-level multi-objective memory architecture exploration problem through a combination of Multi-objective Genetic Algorithm (Memory Architecture exploration) and an efficient heuristic data placement algorithm. At the outer level the memory architecture exploration is done by picking memory modules directly from a ASIC memory Library. This helps in performing the memory architecture exploration in a integrated framework, where the memory allocation, memory exploration and data layout works in a tightly coupled way to yield optimal design points with respect to area, power and performance. We experimented our approach for 3 embedded applications and our approach explores several thousand memory architecture for each application, yielding a few hundred optimal design points in a few hours of computation time on a standard desktop.

Active Vibration Suppression of One-dimensional Nonlinear Structures Using Optimal Dynamic Inversion

A flexible robot arm can be modeled as an Euler-Bernoulli beam which are infinite degrees of freedom (DOF) system. Proper control is needed to track the desired motion of a robotic arm. The infinite number of DOF of beams are reduced to finite number for controller implementation, which brings in error (due to their distributed nature). Therefore, to represent reality better distributed parameter systems (DPS) should be controlled using the systems partial differential equation (PDE) directly. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a controller to suppress nonlinear vibration of a beam. The method used in this paper determines control forces directly from the PDE model of the system. The formulation has better practical significance, because it leads to a closed form solution of the controller (hence avoids computational issues).

An algorithm for dynamic optimal bandwidth allocation in communication networks

We study the problem of optimal bandwidth allocation in communication networks. We consider a queueing model with two queues to which traffic from different competing flows arrive. The queue length at the buffers is observed every T instants of time, on the basis of which a decision on the amount of bandwidth to be allocated to each buffer for the next T instants is made. We consider a class of closed-loop feedback policies for the system and use a twotimescale simultaneous perturbation stochastic approximation(SPSA) algorithm to find an optimal policy within the prescribed class. We study the performance of the proposed algorithm on a numerical setting. Our algorithm is found to exhibit good performance.