(2015 xanvca 28) e"ryz ,zaha f''h

Title:

Optimal Adaptive Control of Uncertain Stochastic Linear Systems

Speaker:

Ilan Rusnak

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Raphael

Time:

Monday, December 28, 2015, 15:30 Refreshments will be served before the seminar

Place:

Room 217, D. Dan and Betty Kahn Bld, Technion

Abstract: The problem of optimal control of stochastic linear time-invariant and time-variant systems with uncertain parameters on finite time interval is formulated. The States and Parameters Observability Canonical (SPOC) form is introduced. This canonical representation of linear systems enables direct application of the existing theory of control and estimation of linear systems, with great simplicity, to the design of the optimal controllers for uncertain linear systems. By the use of the SPOC form the problem of optimal control of stochastic linear systems with uncertain parameters on finite time interval is solved. The solution is explicit and non causal. The solution is composed of the optimal estimator of the augmented state composed of the state of the system and the parameters, and of the optimal LQR controller. The estimator is causal. The controller is non causal as it needs the future outputs and inputs to the plant. This shows the necessity of the systems parameters identification to achieve the goal of optimal control of stochastic systems with uncertain parameters.As a causal approximation to the optimal non causal solution, control schemes based on the certainty equivalence and separation theorems is presented. This causal control schemes are called optimal adaptive control algorithms. The performance of the adaptive control algorithms is analyzed by simulations. The performance is demonstrated in simulation by: (1) application to a hard problem: a 13th order launch vehicle with two unstable poles and three nonminimum phase zeros; and (2) implementation in real time on a motion control system driven by a brush DC motor (with dead-zone and saturation). This demonstrate that the vitality of the optimal adaptive control algorithm.