By Frank L. Lewis, Draguna L. Vrabie, Vassilis L. Syrmos(auth.)
A re-creation of the vintage textual content on optimum keep an eye on theory
As a great introductory textual content and an integral reference, this new version of optimum keep watch over will serve the wishes of either the pro engineer and the complex scholar in mechanical, electric, and aerospace engineering. Its assurance encompasses all of the primary issues in addition to the key adjustments that experience happened lately. An abundance of laptop simulations utilizing MATLAB and proper Toolboxes is integrated to offer the reader the particular event of making use of the speculation to real-world occasions. significant themes coated contain:
Optimal keep an eye on of Discrete-Time Systems
Optimal keep an eye on of Continuous-Time Systems
The monitoring challenge and different LQR Extensions
Final-Time-Free and restricted enter Control
Optimal keep an eye on for Polynomial Systems
Output suggestions and established Control
Robustness and Multivariable Frequency-Domain Techniques
Reinforcement studying and optimum Adaptive Control
Chapter 1 Static Optimization (pages 1–18):
Chapter 2 optimum keep watch over of Discrete?Time platforms (pages 19–109):
Chapter three optimum keep an eye on of Continuous?Time structures (pages 110–176):
Chapter four The monitoring challenge and different LQR Extensions (pages 177–212):
Chapter five Final?Time?Free and restricted enter keep watch over (pages 213–259):
Chapter 6 Dynamic Programming (pages 260–286):
Chapter 7 optimum keep watch over for Polynomial platforms (pages 287–296):
Chapter eight Output suggestions and dependent keep watch over (pages 297–354):
Chapter nine Robustness and Multivariable Frequency?Domain suggestions (pages 355–437):
Chapter 10 Differential video games (pages 438–460):
Chapter eleven Reinforcement studying and optimum Adaptive regulate (pages 461–517):
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Extra resources for Optimal Control, Third Edition
This means that all of our work in part a up through (15) is unchanged by adding to J the ﬁnal-state weighting term. 1-8). Since xN is not constrained to take on an exact value, it can be varied in determining the optimal control. 1-8a) we must have λN = ∂φ = xN − rN . ∂xN (29) The ﬁnal costate is now related to the ﬁnal state xN and the desired ﬁnal state rN by (29); this is our new terminal condition for the solution of (6) and (9). The initial condition is still the given value of xi . Returning to part a and picking up at equation (15), we must now use (29) (instead of (3)) to see that at the ﬁnal time x N = a N x0 − (xN − rN ).
2-6), ∂Hk = Rk uk + BkT λk+1 . 2-7) so the optimal control sequence is determined if we can ﬁnd the costate sequence. A block diagram of the optimal controller appears in Fig. 2-1. We see, however, that it cannot be implemented in this form, since it is not causal. 2-1 State–costate formulation of the discrete linear quadratic optimal controller. 2-4) gives xk+1 = Ak xk − Bk Rk−1 BkT λk+1 . 2-8) At this point we drop the subscripts on the plant and weighting matrices to simplify the notation. The coupled state and costate equations can be written as the single unforced system xk xk+1 A −BR−1 B T = .
2-7) or uk = −Rk−1 BkT λk+1 . 2-47) The initial condition is given as xi , and the ﬁnal state xN is free. This means that xN can be varied in determining the constrained minimum. Hence, dxN = 0. 1-8), then, it is required that λN = ∂φ . 2-48) The ﬁnal state weighting function is φ = 12 xNT SN xN , so that λN = SN xN . 2-28). To solve this two-point boundary-value problem, we shall use the sweep method (Bryson and Ho 1975). 2-50) λk = Sk xk for some intermediate sequence of n × n matrices Sk . 2-50) is a valid assumption.