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The optimal tracking control (OTC) problem for a class of affine nonlinear composite systems with similar structure is considered. By using a modeling technique, the nonlinear similar composite system is first transformed into some quasi-decoupled subsystems. Then the high-order, strongly coupled, nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupled TPBV problems through a successive approximation procedure. The obtained OTC law consists of an accurate linear term and a nonlinear compensation term which is the limit of the adjoint vector sequence. A suboptimal tracking control law is obtained by truncating a finite iterative result of the adjoint vector sequence as its nonlinear compensation term.

Decentralized optimal control for large-scale nonlinear systems with respect to local performance criteria is considered. A decoupled linear Two-Point Boundary Value (TPBV) problem sequence is constructed to approximate the nonlinear coupling large-scale TPBV problem, which is the necessary condition of the nonlinear optimal control problem. We prove that the constructed linear TPBV problem sequence uniformly converges to the nonlinear TPBV problem. By iteratively solving this linear TPBV problem sequence, a decentralized linear feedback optimal control law is obtained. An algorithm is presented to design some qualified approximate optimal control law by using a finite iteration result. An illustrative example shows the validity of the algorithm.

The optimal tracking control (OTC) problem for a class of nonlinear systems with a quadratic performance index is studied. By introducing a sensitivity parameter and expanding the power series around it, the original OTC problem is transformed into a sequence of nonhomogeneous linear two-point boundary value problems. The OTC law obtained consists of an analytic linear feedback term, an analytic linear feedforward term, and a nonlinear compensation term, which is the series sum of the adjoint vector sequence. A reduced-order reference input observer is constructed to make the feedforward term physically realizable. A simulation example is employed to test the validity of the sensitivity approach.

This paper presents a feedforward and feedback controller design approach to solve the problem of optimal control for vehicle active suspension systems with control delay. A quarter-car model with active suspension system is considered. Based on a particular transformation, the original delay system is reduced into a non-delay system. By introducing a disturbance compensation vector, the feedforward and feedback optimal active (FFOA) controller is obtained. The FFOA controller consists of a feedback term and a feedforward term which is to compensate the effect of the load harmonic disturbance. The two terms can be obtained by solving an algebraic Riccati equation and a Sylvester equation respectively. The usefulness and the validity of the proposed controller design mythology are illustrated by a numerical simulation.