Optimal Control SystemsThe theory of optimal control systems has grown and flourished since the 1960's. Many texts, written on varying levels of sophistication, have been published on the subject. Yet even those purportedly designed for beginners in the field are often riddled with complex theorems, and many treatments fail to include topics that are essential to a thorough grounding in the various aspects of and approaches to optimal control. Optimal Control Systems provides a comprehensive but accessible treatment of the subject with just the right degree of mathematical rigor to be complete but practical. It provides a solid bridge between "traditional" optimization using the calculus of variations and what is called "modern" optimal control. It also treats both continuous-time and discrete-time optimal control systems, giving students a firm grasp on both methods. Among this book's most outstanding features is a summary table that accompanies each topic or problem and includes a statement of the problem with a step-by-step solution. Students will also gain valuable experience in using industry-standard MATLAB and SIMULINK software, including the Control System and Symbolic Math Toolboxes. Diverse applications across fields from power engineering to medicine make a foundation in optimal control systems an essential part of an engineer's background. This clear, streamlined presentation is ideal for a graduate level course on control systems and as a quick reference for working engineers. |
Contents
Introduction | 1 |
Discussion on EulerLagrange Equation | 33 |
4 | 39 |
6 | 48 |
Linear Quadratic Optimal Control Systems I | 101 |
Matrix | 109 |
Linear Quadratic Optimal Control Systems II | 151 |
Pontryagin Minimum Principle | 152 |
Additional Necessary Conditions | 259 |
Constrained Optimal Control Systems | 293 |
Vectors and Matrices | 365 |
State Space Analysis | 379 |
MATLAB Files | 385 |
| 415 | |
| 425 | |
| 430 | |
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Common terms and phrases
analytical solution Ax(t boundary conditions Bu(t Calculus of Variations Chapter closed-loop optimal control constraint control law control sequence control system described cost function costate equations Costate System defined differential equations differential Riccati equation discrete-time du(t dx(t dynamic programming eigenvalues Euler-Lagrange equation Example 4.1 fig=fig+1 figure(fig final condition final time tf find the optimal Fixed-Final formulate free-final given Hamiltonian initial condition input k=ko Kalman Lagrangian Linear Quadratic Regulator MATLAB File matrix differential Riccati matrix DRE minimize minimum nonlinear Nyquist plot Obtain the optimal Open-Loop Optimal Control optimal control system Optimal Control Theory optimal control u*(t optimal cost output performance index Phase Plane plant Pontryagin positive definite matrix Procedure Summary relation Riccati Coefficients Riccati equation scalar shown in Figure solve Step symmetric matrix time-invariant tracking system variable vector x(ko x(tf x(to xlabel('t York zero ән дх
Popular passages
Page iii - Namely, because the shape of the whole universe is most perfect and, in fact, designed by the wisest creator, nothing in all of the world will occur in which no maximum or minimum rule is somehow shining forth.
Page 415 - WF DENHAM and AE BRYSON Jr., Optimal Programming Problems with Inequality Constraints. II: Solution by Steepest- Ascent.
References to this book
Control Perspectives on Numerical Algorithms and Matrix Problems Amit Bhaya,Eugenius Kaszkurewicz No preview available - 2006 |