Control design in the time and frequency domain using nonsmooth techniques

Abstract

Significant progress in control design has been achieved by the use of nonsmooth and semiinfinite mathematical programming techniques. In contrast with LMI or BMI approaches, these new methods avoid the use of Lyapunov variables, which gives them two major strategic advances over matrix inequality methods. Due to the much smaller number of decision variables, they do not suffer from size restrictions, and they are much easier to adapt to structural constraints on the controller. In this paper, we further develop this line and address both frequency-and time-domain design specifications by means of a nonsmooth algorithm general enough to handle both cases. Numerical experiments are presented for reliable or fault-tolerant control, and for time response shaping.

Nonsmooth multi-objective synthesis with applications

“…Multi-scenario design addresses this situation by grouping various time-and frequency-domain specifications for several scenarios of the same system into the design. The present work expands on Apkarian and Noll (2006a), Bompart et al (2008), Apkarian et al (2008) and Simões et al (2008) in two main aspects. Time-domain responses to input test signals are those of the nonlinear plant if nonlinear dynamics are available.…”

“…See Bompart et al (2008) and Simões et al (2008) for examples. In (3), k denotes the design variables and k stands for the order of the controller, where the case k ¼ 0 of a static controller is included.…”

“…Nonsmooth optimization has been used recently to solve with success a variety of difficult problems in structured linear controller design (Apkarian & Noll, 2006a;Apkarian, Noll, & Rondepierre, 2008;Bompart, Apkarian, & Noll, 2008;Simões, Apkarian, & Noll, 2008). These design methods avoid using Lyapunov variables whose number grows quadratically with the plant state dimension.…”

Multiple robust H∞ controller design using the nonsmooth optimization method

“…Although nonsmooth approach deals with nonconvex optimization, it has recently received much attention due to the elimination of Lyapunov variables, leading to much faster computations relative to traditional methods. The idea of nonsmooth H ∞ synthesis was initialized in [5][6][7], developed further in [8][9][10], and extended in various directions in [11,12].…”

Stability Optimization of Hybrid Periodic Systems via a Smooth Criterion

“…Other examples are periodically operated simulated moving bed (SMB) processes [25], looping kites [15], or iterative feedback tuning with time and frequency domain constraints [3], [7].…”