Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

Internal control reporting by non-accelerated filers

I examine three issues related to internal control reporting by non-accelerated filers. Motivation for the three studies comes from the fact that Section 404 of the Sarbanes-Oxley Act (SOX) continues to be controversial, as evidenced by the permanent exemption from Section 404(b) of SOX granted to non-accelerated filers by the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010. The Dodd-Frank Act also requires the SEC to study compliance costs associated with smaller accelerated filers. In the first part of my dissertation, I document that the audit fee premium for non-accelerated filers disclosing a material weakness in internal controls (a) is significantly lower than the corresponding premium for accelerated filers, and (b) declines significantly over time. I also find that in the case of accelerated filers remediating clients pay lower fees compared to clients continuing to report internal control problems; however, such differences are not observed in the case of non-accelerated filers. The second essay focuses on audit report lag. The results indicate that presence of material weaknesses are associated with increased audit report lags, for both accelerated and non-accelerated filers. The results also indicate that the decline in report lag following remediation of problems is greater for accelerated filers than for non-accelerated filers. The third essay examines early warnings (pursuant to Section 302 disclosures) for firms that subsequently disclosed internal control problems in their 404 reports. The analyses indicate that non-accelerated firms with shorter CFO tenure, presence of accounting experts on the audit committee, and more frequent audit committee meetings are more likely to provide prior Section 302 warnings. Overall the results suggest that there are differences in internal control reporting between the accelerated and non-accelerated filers. The results provide empirical grounding for the ongoing debate about internal control reporting by non-accelerated filers.

Branch and Bound algorithms in greenhouse climate control

The horticultural sector has become an increasingly important sector of food production, for which greenhouse climate control plays a vital role in improving its sustainability. One of the methods to control the greenhouse climate is Model Predictive Control, which can be optimized through a branch and bound algorithm. The application of the algorithm in literature is examined and analyzed through small examples, and later extended to greenhouse climate simulation. A comparison is made of various alternative objective functions available in literature. Subsequently, a modidified version of the B&B algorithm is presented, which reduces the number of node evaluations required for optimization. Finally, three alternative algorithms are developed and compared to consider the optimization problem from a discrete to a continuous control space.

Shortcuts to adiabaticity in the double well

123 p.

DATA DRIVEN INTELLIGENT AGENT NETWORKS FOR ADAPTIVE MONITORING AND CONTROL

To analyze the characteristics and predict the dynamic behaviors of complex systems over time, comprehensive research to enable the development of systems that can intelligently adapt to the evolving conditions and infer new knowledge with algorithms that are not predesigned is crucially needed. This dissertation research studies the integration of the techniques and methodologies resulted from the fields of pattern recognition, intelligent agents, artificial immune systems, and distributed computing platforms, to create technologies that can more accurately describe and control the dynamics of real-world complex systems. The need for such technologies is emerging in manufacturing, transportation, hazard mitigation, weather and climate prediction, homeland security, and emergency response. Motivated by the ability of mobile agents to dynamically incorporate additional computational and control algorithms into executing applications, mobile agent technology is employed in this research for the adaptive sensing and monitoring in a wireless sensor network. Mobile agents are software components that can travel from one computing platform to another in a network and carry programs and data states that are needed for performing the assigned tasks. To support the generation, migration, communication, and management of mobile monitoring agents, an embeddable mobile agent system (Mobile-C) is integrated with sensor nodes. Mobile monitoring agents visit distributed sensor nodes, read real-time sensor data, and perform anomaly detection using the equipped pattern recognition algorithms. The optimal control of agents is achieved by mimicking the adaptive immune response and the application of multi-objective optimization algorithms. The mobile agent approach provides potential to reduce the communication load and energy consumption in monitoring networks. The major research work of this dissertation project includes: (1) studying effective feature extraction methods for time series measurement data; (2) investigating the impact of the feature extraction methods and dissimilarity measures on the performance of pattern recognition; (3) researching the effects of environmental factors on the performance of pattern recognition; (4) integrating an embeddable mobile agent system with wireless sensor nodes; (5) optimizing agent generation and distribution using artificial immune system concept and multi-objective algorithms; (6) applying mobile agent technology and pattern recognition algorithms for adaptive structural health monitoring and driving cycle pattern recognition; (7) developing a web-based monitoring network to enable the visualization and analysis of real-time sensor data remotely. Techniques and algorithms developed in this dissertation project will contribute to research advances in networked distributed systems operating under changing environments.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

An optimization-based algorithm for shunt active filter under distorted supply voltages

When the supply voltages are balanced and sinusoidal, load compensation can give both unity power factor (UPF) and perfect harmonic cancellation (PHC) source currents. But under distorted supply voltages, achieving both UPF and PHC currents are not possible and contradictory to each other. Hence there should be an optimal performance between these two important compensation goals. This paper presents an optimal control algorithm for load compensation under unbalanced and distorted supply voltages. In this algorithm source currents are compensated for reactive, imbalance components and harmonic distortions set by the limits. By satisfying the harmonic distortion limits and power balance, this algorithm gives the source currents which will provide the maximum achievable power factor. The detailed simulation results using MATLAB are presented to support the performance of the proposed optimal control algorithm.

Increasing underwater vehicle autonomy by reducing energy consumption

In this paper, we concern ourselves with finding a control strategy that minimizes energy consumption along a trajectory connecting two given configurations. We develop an algorithm, based on our previous work with the time optimal problem, which provides implementable control strategies that are energy efficient. We find an interesting correlation between the duration of these trajectories and the optimal duration. We present the algorithm, control strategy and experimental results from our test-bed vehicle.

Implementation results of efficient trajectories on a testbed AUV

In this paper we consider the implementation of time and energy efficient trajectories onto a test-bed autonomous underwater vehicle. The trajectories are losely connected to the results of the application of the maximum principle to the controlled mechanical system. We use a numerical algorithm to compute efficient trajectories designed using geometric control theory to optimize a given cost function. Experimental results are shown for the time minimization problem.

Practical application of pseudospectral optimization to robot path planning

To obtain minimum time or minimum energy trajectories for robots it is necessary to employ planning methods which adequately consider the platform’s dynamic properties. A variety of sampling, graph-based or local receding-horizon optimisation methods have previously been proposed. These typically use simplified kino-dynamic models to avoid the significant computational burden of solving this problem in a high dimensional state-space. In this paper we investigate solutions from the class of pseudospectral optimisation methods which have grown in favour amongst the optimal control community in recent years. These methods have high computational efficiency and rapid convergence properties. We present a practical application of such an approach to the robot path planning problem to provide a trajectory considering the robot’s dynamic properties. We extend the existing literature by augmenting the path constraints with sensed obstacles rather than predefined analytical functions to enable real world application.