Institute for Systems Research
Permanent URI for this communityhttp://hdl.handle.net/1903/4375
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Item Partially Observed Differential Games, Infinite Dimensional HJI Equations, and Nonlinear HControl(1994) James, Matthew R.; Baras, John S.; ISRThis paper presents new results for partially observed nonlinear differential games, which are applied to the nonlinear output feedback Hrobust control problem. Using the concept of information state, we solve these problems in terms of an infinite dimensional partial differential equation, viz., the Hamilton-Jacobi-Isaacs equation for partial observed differential games. We give definitions of smooth and viscosity solutions, and prove that the value function is a viscosity solution of the HJI equation. We prove a verification theorem, which implies that the optimal controls are separated in that they depend on the observations through the information state. This constitutes a separation principle for partially observed differential games. We also present some new results concerning the certainty equivalence principle.Item Robust Output Feedback Control for Discrete - Time Nonlinear Systems(1993) James, Matthew R.; Baras, John S.; ISRIn this paper we present a new approach to the solution of the output feedback robust control problem. We employ the recently developed concept of information state for output feedback dynamic games, and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state. The resulting controller is an information state feedback controller, and is intrinsically infinite dimensional. Stability results are obtained using the theory of dissipative systems, and indeed, our results are expressed in terms of dissipation inequalities.Item Output Feedback Risk - Sensitive Control and Differential Games for Continuous - Time Nonlinear Systems(1993) James, Matthew R.; Baras, John S.; Elliott, Robert J.; ISRIn this paper we carry out a formal analysis of an output feedback risk-sensitive stochastic control problem. Using large deviation limits, this problem is related to a deterministic output feedback differential game. Both problems are solved using appropriate information states. The use of an information state for the game problem is new, and is the principal contribution of our work. Our results have implications for the nonlinear robust stabilization problem.