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Design of closed-loop optimal controllers for systems with shape deterministic inputs

The design of closed-loop optimal controllers for systems with output-feedback is considered. The disturbance, initial condition and reference signals in the system are assumed to be either deterministic or shape-deterministic or a sum of both, The shape-deterministic signals have a specified time response, but the magnitude of the response is a random variable with known mean and covariance. The performance criterion includes the expectation averaging operator, and the cost is measured over the positive-time interval only. The performance criterion also includes dynamical operators which may be chosen to achieve specified response characteristics. The solution for the closed-loop controller is obtained, for both tracking and regulating problems, in the s-domain. The controller is not, in general, the same as those obtained from either the LQP or LQG optimal-control problems. The advantages of the technique are that output feedback, rather than state-feedback, is used, and both random and deterministic signals are optimised. In other approaches to such problems, there are severe difficulties in defining a performance criterion which is suitable for both deterministic and stochastic signals.