Optimal control for state-space models

  • M. H. A. Davis
  • R. B. Vinter
Part of the Monographs on Statistics and Applied Probability book series (MSAP)


This chapter concerns optimal control problems for the state-space models discussed in Chapters 2 and 3. The state and observation processes x k and y k are given respectively by the equations
$${x_{k + 1}} = A(k){x_k} + B(k){u_k} + C(k){w_k}$$
$${y_k} = H(k){x_k} + G(k){w_k}$$
where w k is a white-noise sequence. We now wish to choose the control sequence u k so that the system behaves in some desirable way. We have to settle two questions at the outset, namely what sort of controls are to be allowed (or, are admissible) and what the control objective is.


Kalman Filter Riccati Equation Average Cost Bellman Equation Algebraic Riccati Equation 
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Copyright information

© M. H. A. Davis and R. B. Vinter 1985

Authors and Affiliations

  • M. H. A. Davis
    • 1
  • R. B. Vinter
    • 1
  1. 1.Department of Electrical EngineeringImperial CollegeLondonUK

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