Hybrid Estimation of State and Input for Linear Continuous Time-varying Systems: A Game Theory Approach
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摘要: The $H_\infty$ hybrid estimation problem for linear continuous time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. Based on the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in\hfill terms\hfill of\hfill solutions\hfill to\hfill a\hfill Riccati\hfill diffe-\\rential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix that reflects the internal relations between the unknown input and output estimation error. Both state and unknown inputs estimation are realized by the proposed estimator. Thus, the results in this paper are also capable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numerical example is provided to illustrate the proposed approach.Abstract: The $H_\infty$ hybrid estimation problem for linear continuous time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. Based on the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in\hfill terms\hfill of\hfill solutions\hfill to\hfill a\hfill Riccati\hfill diffe-\\rential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix that reflects the internal relations between the unknown input and output estimation error. Both state and unknown inputs estimation are realized by the proposed estimator. Thus, the results in this paper are also capable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numerical example is provided to illustrate the proposed approach.
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Key words:
- Time-varying system /
- input estimation /
- game theory /
- Riccati equation
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