Hybrid Estimation of State and Input for Linear Continuous Time-varying Systems:A Game Theory Approa

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The H∞ hybrid estimation problem for linear continuous time-varying systems is in-vestigated in this paper, where estimated signals are linear combination of state and input. Designobjective requires the worst-case energy gain from disturbance to estimation error be less than a pre-scribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-playerzero sum di?erential game. Based on the di?erential game approach, necessary and su?cient solvableconditions for the hybrid estimation problem are provided in terms of solutions to a Riccati di?e-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 re?ects theinternal relations between the unknown input and output estimation error. Both state and unknowninputs estimation are realized by the proposed estimator. Thus, the results in this paper are alsocapable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numericalexample is provided to illustrate the proposed approach. The H∞ hybrid estimation problem for linear continuous time-varying systems is in-vestigated in this paper, where estimated signals are linear combination of state and input. Design objectivejective the worst-case energy gain from disturbance to estimation error be less than a pre -defined level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum di? ential game. Based on the di? erential game approach, necessary and su? cient solvableconditions for the hybrid estimation problem are provided in terms of solutions to a Riccati di? e-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 re? ects the internal relations between the unknown input and output estimation error. Both state and unknown input estimates are realized by the proposed estimator. Thus, the results in this paper are alsocapable of dealing with faul t diagnosis problems of linear time-varying systems. At last, a numeric example is provided to illustrate the proposed approach.
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