1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

For many types of machine learning algorithms, one can compute the statistically "optimal" way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are computationally expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate. Empirically, we observe that the optimality criterion sharply decreases the number of training examples the learner needs in order to achieve good performance.

Active learning with statistical models

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and moving-horizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

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Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Theory and applications of adaptive control-A survey

Model predictive control algorithms achieve offset-free control objectives by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant-model mismatch and/or unmodeled disturbances. Its effectiveness has been proven for particular square cases only. For systems with a number of measured variables (p) greater than the number of manipulated variables (m), it is clear that any controller can track without offset at most m controlled variables. One may think that m integrating disturbances are sufficient to guarantee offset-free control in the m controlled variables. We show this idea is incorrect and present general conditions that allow zero steady-state offset. In particular, a number of integrating disturbances equal to the number of measured variables are shown to be sufficient to guarantee zero offset in the controlled variables. These results apply to square and nonsquare, open-loop stable, integrating and unstable systems.

Disturbance models for offset‐free model‐predictive control

INTRODUCTION Classical and Modern Control Optimization Optimal Control Historical Tour About This Book Chapter Overview Problems CALCULUS OF VARIATIONS AND OPTIMAL CONTROL Basic Concepts Optimum of a Function and a Functional The Basic Variational Problem The Second Variation Extrema of Functions with Conditions Extrema of Functionals with Conditions Variational Approach to Optimal Systems Summary of Variational Approach Problems LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS I Problem Formulation Finite-Time Linear Quadratic Regulator Analytical Solution to the Matrix Differential Riccati Equation Infinite-Time LQR System I Infinite-Time LQR System II Problems LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS II Linear Quadratic Tracking System: Finite-Time Case LQT System: Infinite-Time Case Fixed-End-Point Regulator System Frequency-Domain Interpretation Problems DISCRETE-TIME OPTIMAL CONTROL SYSTEMS Variational Calculus for Discrete-Time Systems Discrete-Time Optimal Control Systems Discrete-Time Linear State Regulator Systems Steady-State Regulator System Discrete-Time Linear Quadratic Tracking System Frequency-Domain Interpretation Problems PONTRYAGIN MINIMUM PRINCIPLE Constrained Systems Pontryagin Minimum Principle Dynamic Programming The Hamilton-Jacobi-Bellman Equation LQR System using H-J-B Equation CONSTRAINED OPTIMAL CONTROL SYSTEMS Constrained Optimal Control TOC of a Double Integral System Fuel-Optimal Control Systems Minimum Fuel System: LTI System Energy-Optimal Control Systems Optimal Control Systems with State Constraints Problems APPENDICES Vectors and Matrices State Space Analysis MATLAB Files REFERENCES INDEX

Richard C. Dorf

Papers

Optimal Control Systems