Continuous Time Dynamical Systems

Chapter 4

Linear Optimal Control Systems Incorporating Observers

Using BPFs and SLPs two recursive algorithms are presented for the analysis of linear time-invariant optimal control systems incorporating observers. An illustrative example is included to demonstrate the superiority of recursive algorithms over the non-recursive approaches.

4.1    Introduction

Consider a linear time-invariant completely observable and completely controllable system described by

$\dot{\mathbf{\text{x}}}\left(t\right)=A\mathbf{\text{x(}}t)+B\mathbf{\text{u(}}t)$

(4.1)

$\mathbf{\text{y}}\left(t\right)=C\mathbf{\text{x(}}t)$

(4.2)

where u(t), x(t) and y(t) are the plant input, state, and output vectors, respectively, and A, B and C are n × n, n × r and p × n real, constant matrices, respectively. Assume that rank of C is p. An observer described by

$\dot{\mathbf{\text{z}}}\left(t\right)=F\mathbf{\text{z(}}t)$