## 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. |

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good explanation

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Beware of the staggering number of typos in this book!

New concepts and variables are introduced only as letters. Qualitative discussion describing what is being done is skipped. It's just cold math.

### Contents

Introduction | 1 |

Calculus of Variations and Optimal Control | 19 |

Linear Quadratic Optimal Control Systems I | 101 |

Optimal Controls | 141 |

Linear Quadratic Optimal Control Systems II | 151 |

DiscreteTime Optimal Control Systems | 191 |

Pontryagin Minimum Principle | 249 |

Constrained Optimal Control Systems | 293 |

Constraints | 351 |

Vectors and Matrices | 365 |

State Space Analysis | 379 |

MATLAB Files | 385 |

415 | |

425 | |

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### Common terms and phrases

analytical solution becomes boundary conditions calculus of variations Chapter closed-loop optimal control Consider constraint control law control sequence control system described cost function costate equations Costate System defined differential equations differential Riccati equation discrete-time dynamic programming eigenvalues Energy-Optimal Control Euler-Lagrange equation Example 4.1 extrema final condition Final State 0,0 final time tf find the closed-loop find the optimal Fixed-Final formulate Hamiltonian hence HJB equation Implementation increment initial condition input Kalman Lagrange multiplier Lagrangian Let us note Linear Quadratic Regulator loop optimal MATLAB matrix differential Riccati matrix DRE minimum nonlinear Nyquist plot Obtain the optimal Open-Loop Optimal Control optimal condition optimal control system optimal control u*(t optimal cost output P(fc performance index Phase-Plane Trajectory plot positive definite matrix Procedure Summary Riccati Coefficients scalar shown in Figure SIMULINK Step symmetric symmetric matrix time-invariant Time-Optimal Control System unconstrained variable vector x(fc xlabel('t zero

### Popular passages

Page 417 - 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 |