Suboptimal control for nonlinear systems: a successive approximation approach

Tang, Gong‐You

doi:10.1016/j.sysconle.2004.09.012

Cited by 134 publications

(83 citation statements)

References 7 publications

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“…By using the successive approximation approach [26,27,31,34], we construct the adjoint vector sequence …”

Section: Theoremmentioning

confidence: 99%

“…It can be proved that the adjoint vector solution sequence { ( ) ( )} in (25) uniformly converges to ( ), and the state vector solution sequence { ( ) ( )} in (26) uniformly converges to ( ) [26,27,31,34].…”

Section: Theoremmentioning

confidence: 99%

“…Secondly, for the AUVs heading control system, the coupled TPBV problem is derived from the maximum principle of optimal control theory. Then by using a successive approximation approach [26,27], the coupled TPBV problem is transformed into solving two decoupled linear differential sequences in state vectors and adjoint vectors. By iterative solution, the ODRC law is obtained, and a Luenberger disturbances observer is constructed to make it realizable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Disturbances Rejection Control for Autonomous Underwater Vehicles in Shallow Water Environment

Yang

Tang

et al. 2017

Mathematical Problems in Engineering

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To deal with the disturbances of wave and current in the heading control of Autonomous Underwater Vehicles (AUVs), an optimal disturbances rejection control (ODRC) approach for AUVs in shallow water environment is designed to realize this application. Based on the quadratic optimal control theory, the AUVs heading control problem can be expressed as a coupled two-point boundary value (TPBV) problem. Using a recently developed successive approximation approach, the coupled TPBV problem is transformed into solving a decoupled linear state equation sequence and a linear adjoint equation sequence. By iteratively solving the two equation sequences, the approximate ODRC law is obtained. A Luenberger observer is constructed to estimate wave disturbances. Simulation is provided to demonstrate the effectiveness of the presented approach.

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“…By using the successive approximation approach [26,27,31,34], we construct the adjoint vector sequence …”

Section: Theoremmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Disturbances Rejection Control for Autonomous Underwater Vehicles in Shallow Water Environment

Yang

Tang

et al. 2017

Mathematical Problems in Engineering

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“…Therefore, finding an approximate optimal control law is one of the important aims of researchers. Recently, Tang [4][5][6] proposed approximation approaches to generating a suboptimal control law, which can avoid the complexity of solving TPBV problems with time-delay or nonlinear terms. Systems with exogenous persistent disturbances are quite common in practice.…”

Section: Introductionmentioning

confidence: 99%

Optimal Tracking Control for Discrete Time‐delay Systems With Persistent Disturbances

Tang¹,

Sun²,

Liu³

2006

Asian Journal of Control

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Optimal tracking control (OTC) for discrete time-delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time-advance on time-delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.

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“…Thus, obtaining an approximate optimal control law is currently one of the important aims of researchers. So far, successive approximate approach [4][5][6] and sensitivity approach [7] have been applied.…”

Section: Introductionmentioning

confidence: 99%

Optimal Rejection With Zero Steady‐state Error of Sinusoidal Disturbances for Time‐delay Systems

Tang¹,

Zhang²

2006

Asian Journal of Control

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This paper studies the problem of optimal rejection with zero steady-state error of sinusoidal disturbances for linear systems with time-delay. Based on the internal model principle, a disturbance compensator is constructed to counterbalance the external sinusoidal disturbances, so that the original system can be transformed into an augmented system without disturbances. Then, with the introduction of a sensitivity parameter and expanding power series around it, the optimal disturbance rejection problem can be simplified to the problem of solving an infinite sum of a linear optimal control series without timedelay or disturbance. The optimal control law for disturbance rejection with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. In the presented approach, iteration is required only for the time-delay compensation series. By intercepting a finite sum of the compensation series, we obtain an approximate physically realizable optimal control law that avoids complex calculation. A numerical simulation shows that the algorithm is effective and easy to implement.

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Suboptimal control for nonlinear systems: a successive approximation approach

Cited by 134 publications

References 7 publications

Optimal Disturbances Rejection Control for Autonomous Underwater Vehicles in Shallow Water Environment

Optimal Disturbances Rejection Control for Autonomous Underwater Vehicles in Shallow Water Environment

Optimal Tracking Control for Discrete Time‐delay Systems With Persistent Disturbances

Optimal Rejection With Zero Steady‐state Error of Sinusoidal Disturbances for Time‐delay Systems

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