An actively adaptive control for linear systems with random parameters via the dual control approach
- 1 April 1973
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 18 (2), 109-117
- https://doi.org/10.1109/tac.1973.1100242
Abstract
A new method is presented for controlling a discrete-time linear system with possibly time-varying random parameters in the presence of input and output noise. The cost is assumed to be quadratic in the state and control. Previous algorithms for the above problem when the system had both zeros and poles unknown were of the open-loop feedback type, i.e., they did not take into account that future observations will be made. Therefore, even though these schemes were adaptive, their learning was "accidental." In contrast to this, the new approach uses an expression of the optimal cost-to-go that exhibits the dual purpose of the control, i.e., learning and control. The effect of the present control on the future estimation ("learning") appears explicitly in the cost used in the stochastic dynamic programming equation. The resulting sequence of controls, which is of the closed-loop type, is shown via simulations to appropriately divide its energy between the learning and the control purposes. Therefore, this control is called actively adaptive because it regulates the speed and amount of learning as required by the performance index. The simulations on a third-order system with six unknown parameters also demonstrate the computational feasibility of the proposed algorithm.Keywords
This publication has 12 references indexed in Scilit:
- Parameter identification and control of linear discrete-time systemsIEEE Transactions on Automatic Control, 1972
- Adaptive stochastic control for a class of linear systemsIEEE Transactions on Automatic Control, 1972
- Optimal adaptive control of linear systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1971
- A parameter-adaptive control techniqueAutomatica, 1969
- A new algorithm for suboptimal stochastic controlIEEE Transactions on Automatic Control, 1969
- On the optimal control of discrete-time linear systems with random parametersIEEE Transactions on Automatic Control, 1969
- Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurementsIEEE Transactions on Automatic Control, 1968
- Optimum control of an unknown linear plant using Bayesian estimation of the errorIEEE Transactions on Automatic Control, 1965
- Some Types of Optimal Control of Stochastic SystemsJournal of the Society for Industrial and Applied Mathematics Series A Control, 1964
- Adaptive Control ProcessesPublished by Walter de Gruyter GmbH ,1961