Steady-State Robust Optimal Control and Filtering for Input/Output Time-Delay Systems
|Course||Control Theory and Control Engineering|
|Keywords||Time-delay systems Reorganized innovation Krein space Spectral factorization Diophantine equation Riccati equation|
Time-delay systems are of wide application background, and are available in many engineering fields such as signal processing in wireless sensor networks, communication systems, and congestion control in networks. Hence, the control and filtering problems for the time-delay systems have been intriguing many researchers for decades. However, some problems upon fundamental theory remain unsettled as a great challenge, and the conventional approaches, covering state augmentation method, partial differential equation method and linear operator theory, etc, tend to consume enormous or complicated calculations and the results from them are hard to make further performance analysis. The control and filtering problems for the time-delay systems thus remain to be perfected further.The dissertation focuses on the steady-state optimal filtering, the steady-state H_∞filtering, robust optimal estimation for time-delay systems and the steady-state linear quadratic optimal control for input delay systems, and the main results are as follows.It poses a novel method of the spectral factorization, resolves the steady-state optimal filtering problem for systems with time-delay measurements, and designs the steady-state optimal filter by solving a Diophantine equation and a left spectral factorization. Compared with the state augmentation method, the presented approach is much simpler for derivation and calculation, especially when the time-delay is large.It discusses the steady-state H_∞filtering problem, transforms the underlying problem into an indefinite quadratic optimal one in Krein space, makes use of the theory in Krein space and the reorganized innovation analysis, performs a J-spectral factorization, and achieves the steady-state H_∞filter and the sufficient and necessary condition.It considers the optimal robust estimation problem for time-delay systems with stochastic uncertainties. By introducing fictitious noise and taking advantage of the reorganized innovation analysis, the optimal robust estimator is designed via solving Riccati equations and a Lyapunov equation.It investigates the steady-state linear quadratic optimal control problem for systems with multiple input delays, converts the original problem into solving a Diophantine equation and a right spectral factorization utilizing polynomial approach, and proposes a new method for the spectral factorization, which is realized by constructing a backward stochastic model, applying the reorganized innovation technique and finally solving Riccati equations with the same dimension as the original systems.It is the first attempt to propose the novel spectral factorization method by applying the reorganized innovation analysis and Krein space theory and settles the steady-state linear quadratic optimal control and filtering problems for the systems with input/output delays effectively. The numerical experiments show that the approaches posed are all very effective and superior to other ones as the systems are with the larger or more delays.