| This research has produced a numerical algorithm for the design of a finite dimensional compensator for partially observed, hyperbolic systems with boundary/point control. The necessity of a finite dimensional compensator, which is a control law generated only from information on an estimate of the state variable, is motivated from the standpoint of implementation. The original system is infinite dimensional by nature, and practicality dictates that the compensator be finite dimensional. Moreover, the methods used to design the compensator entail the use of certain design parameters which allow the designer to shape both the feedback and estimator gains to achieve various performance criteria such as margin of stability. A numerical scheme is developed such that certain necessary uniform stabilizability and uniform trace regularity conditions are inherently satisfied by the chosen numerical scheme. This is particularly important since the design of the finite dimensional estimator and compensator on solutions to appropriate algebraic Riccati equations (ARE) and the stability of the solutions to the corresponding sequence of AREs, with bounded and unbounded coefficients, depends on these stabilizability conditions. Hence, a method is developed to construct a finite-dimensional compensator based upon both a certain regularization scheme applied to the original problem and an approximation algorithm applied to the regularized problem. This method produces a finite dimensional compensator that uniformly maintains the control theoretic properties of the original closed loop system, such as a desired level of performance and asymptotic stability properties. Results from a numerical simulation of the theory are provided. |
