Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

Abstract

A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.

Optimal parallel-distributed-compensation controller design for a class of time-varying Takagi–Sugeno fuzzy model–based time-delay systems by using the orthogonal function approach–assisted genetic algorithm

“…However, the LMI method (Chou et al, 2006; Guan and Chen, 2004) cannot be used to design time-varying TS fuzzy model–based time-delay control systems with quadratic-optimal PDC controllers. Although genetic algorithms (GAs) can be used to solve complex static optimization problems (Chou and Cheng, 2019), they are very difficult to use for dynamic optimization when designing quadratic optimal PDC controllers for time-varying TS fuzzy model–based time-delay control systems. To the best of our knowledge, no studies have proposed designs for time-varying TS fuzzy model–based time-delay control systems with quadratic optimal PDC controllers.…”