New method for composite optimal control of singularly perturbed systems. (English) Zbl 0892.49025
Summary: In this paper, a new method, based on a generalized algebraic Riccati equation arising in descriptor systems, is presented to solve the composite optimal control problem of singularly perturbed systems. Contrary to the existing method, the slow subsystem is viewed as a special kind of descriptor system. A new composite optimal controller is obtained which is valid for both standard and non-standard singularly perturbed systems. It is shown that the composite optimal control can be obtained simply by revising the solution of the slow regulator problem. It is proven that the composite optimal control can achieve a performance which is \(O(\varepsilon^2)\) close to the optimal performance. Although this result is well-known for the standard singularly perturbed systems, it is new in the non-standard case. The equivalence between the new composite optimal controller and the existing one is also established for the standard singularly perturbed systems.
MSC:
| 49N35 | Optimal feedback synthesis |
| 93C99 | Model systems in control theory |
| 49L20 | Dynamic programming in optimal control and differential games |
Keywords:
Riccati equation; descriptor systems; composite optimal control problem; singularly perturbed systems; slow regulator problemReferences:
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