Robust Design of Nonlinear Control Systems

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In this year, we have obtained the following results.1.The nonlinear non-standard H^* control problem is studied. In this research, two cases are concerned with : (a) the case in which the direct-through term from the input to the output does not have full-rank, and (b) the case in which the direct-through term from the disturbance to the measurement output does not have full-rank. In these cases, the square compliment cannot be carried out with the usual method, and thus the Hamilton-Jacobi-Issacs partial differential inequality is not well-defined. To resolve this difficulty, the term includes undecided function is added to the dissipative inequality, which makes the direct-through term have full-rank. The function is determined as the added term is equal to zero, and substitutes the undecided function in the Hamilton-Jacobi-Issacs partial differential inequality. Therefore the sufficient conditions for the cases (a) and (b) are obtained.2.The stability condition of the linear systems which includes uncertain parameters nonlinearly is studied. The mapping theorem is extended to the case that the assumption of the monotonicity with respect to the uncertain parameters holds, while the original mapping theorem assumes the multi-linearity. By means of the extended mapping theorem the sufficient condition of stability is derived. Also the sufficient condition of monotonicity is obtained.3.In the MIMO nonlinear system of which the vector relative degree cannot be defined, the robust vector relative degree is defined. The control law is derived using the robust vector relative degree, and it achieves BIBS stability of the control system.4.To run the above control laws on computers, a new nonlinear digital-redesign method is developed, which ensures the precision of third order with respect to the sampling interval.