Linear Quadratic Optimal Control of Time-Varying Systems with Indefinite Costs on Hilbert Spaces

1999 ◽  
Vol 12 (2) ◽  
pp. 196-218
Author(s):  
Birgit Jacob
Keyword(s):  
Optimal Control ◽  
Hilbert Spaces ◽  
Time Varying ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Time Varying Systems ◽  
Quadratic Optimal Control

Receding Time Horizon Linear Quadratic Optimal Control for Multi-Axis Contour Tracking Motion Control1

1998 ◽  
Vol 122 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Robert J. McNab ◽  
Tsu-Chin Tsao
Keyword(s):  
Optimal Control ◽  
Time Horizon ◽  
Tracking Error ◽  
Design Parameters ◽  
Control Input ◽  
Contour Tracking ◽  
Time Varying ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

A receding time horizon linear quadratic optimal control approach is formulated for multi-axis contour tracking problem. The approach employs a performance index with fixed weights on quadratic contouring error, tracking error, and control input over a future finite horizon. The problem is then cast into a standard receding horizon LQ problem with time varying weighting matrices, which are functions of the future contour trajectory within the horizon. The formulation thus leads to a solution of time varying state feedback and finite preview gains. Stability is proven for the linear trajectory case. Experimental and simulated results for an X-Y motion control problem are presented, which demonstrate the effectiveness of the control scheme and the effects of the key controller design parameters. [S0022-0434(00)01202-8]

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