Assessing alternative control strategies for systems with asymptotically stable equilibrium positions
| Autor: | I. E. Egorov |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Lyapunov function
Mathematical optimization Control and Optimization Optimal control Pontryagin's minimum principle Human-Computer Interaction Computational Mathematics symbols.namesake Exponential stability Control theory Ordinary differential equation Stability theory symbols Alternative control Hamiltonian (control theory) Mathematics |
| Zdroj: | Moscow University Computational Mathematics and Cybernetics. 37:112-120 |
| ISSN: | 1934-8428 0278-6419 |
| DOI: | 10.3103/s0278641913030059 |
| Popis: | In a number of optimal control applications, it is possible to arrange control guided only by an analysis of a system’s dynamic properties. These controls are customarily referred to as alternatives to those that satisfy the Pontryagin maximum principle. This work considers autonomous systems of ordinary differential equations with a terminal objective functional that at each fixed value of the control parameter have unique and asymptotically stable equilibrium positions. It is shown that the problem of arranging alternative control can then be reduced to a finite-dimensional problem of mathematical programming. An estimate of the alternative control error in terms of the objective functional is obtained. Sufficient conditions for obtaining this estimate are given. A mathematical model of leukemia therapy is considered as an example. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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