Robust singular optimization for linear time varying systems by integral high-order sliding mode

This paper presents an approach to solve a singular quadratic optimization problem for linear time varying systems based on the so‐called integral high‐order sliding mode control. The plant which is time varying is affected for some bounded disturbances, and the criterion to minimize is degenerated, in the sense that the weighting matrix can possess any rank. It is shown the natural connection between the order of singularity of the time varying quadratic criterion, which is connected to the rank of the cost matrix and the order of the sliding mode. An integral high‐order sliding mode is proposed to control the behavior of the transit phase before arriving toward the corresponding higher order singular time varying optimal manifold in prescribed time. The transformation to the phase‐variable form for the Linear Time Variant Systems (LTVS) becomes the key step to solve the problem, and the proposed solution provides the insensitivity of trajectory w.r.t. matched bounded uncertainties. Such a design is applied to a probe landing problem to illustrate the effectiveness of the proposed approach.