Robust stabilization for uncertain switched impulsive control systems with state delay: An LMI approach

This paper deals with the problem of robust H_∞ state feedback stabilization for uncertain switched linear systems with state delay. The system under consideration involves time delay in the state, parameter uncertainties and nonlinear uncertainties. The parameter uncertainties are norm-bounded time-varying uncertainties which enter all the state matrices. The nonlinear uncertainties meet with the linear growth condition. In addition, the impulsive behavior is introduced into the given switched system, which results a novel class of hybrid and switched systems called switched impulsive control systems. Using the switched Lyapunov function approach, some sufficient conditions are developed to ensure the globally robust asymptotic stability and robust H_∞ disturbance attenuation performance in terms of certain linear matrix inequalities (LMIs). Not only the robustly stabilizing state feedback H_∞ controller and impulsive controller, but also the stabilizing switching law can be constructed by using the corresponding feasible solution to the LMIs. Finally, the effectiveness of the algorithms is illustrated with an example.     

Efficient robust optimization for robust control with constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed linear constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program. While the reparameterized problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of per iteration of an interior-point method. We focus on the case when the disturbance set is ∞-norm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primal-dual interior-point methods in which each iteration requires time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, that illustrate the efficiency of this approach.     

Robust optimal control for a batch nonlinear enzyme-catalytic switched time-delayed process with noisy output measurements

In this paper, we consider a nonlinear switched time-delayed (NSTD) system with an unknown time-varying function describing the batch culture. The output measurements are noisy. According to the actual fermentation process, this time-varying function appears in the form of a piecewise-linear function with unknown kinetic parameters and switching times. The quantitative definition of biological robustness is given to overcome the difficulty of accurately measuring intracellular material concentrations. Our main goal is to estimate these unknown quantities by using noisy output measurements and biological robustness. This estimation problem is formulated as a robust optimal control problem (ROCP) governed by the NSTD system subject to continuous state inequality constraints. The ROCP is approximated as a sequence of nonlinear programming subproblems by using some techniques. Due to the highly complex nature of these subproblems, we propose a hybrid parallel algorithm, based on Nelder–Mead method, simulated annealing and the gradients of the constraint functions, for solving these subproblems. The paper concludes with simulation results.     

Robust forward backward based beamformer for a general-rank signal model with real-valued implementation

A robust forward backward (FB) beamformer for an incoherently scattered general-rank signal model with real-valued implementation is proposed based on the uniform linear array (ULA) structure by introducing a preprocessing transformation matrix. With the preprocessing, the computational complexity is reduced significantly due to a real-valued close-form solution for the optimum weight vector; furthermore, the proposed algorithm can achieve a higher output SINR (signal-to-interference-plus-noise ratio) and has lower sensitivity to the diagonal-loading parameters especially for low input SNR (signal-to-noise ratio) scenarios.     

Perturbation and robust stability of autonomous singular linear matrix difference equations

In the perturbation theory of linear matrix difference equations, it is well known that the theory of finite and infinite elementary divisors of regular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them to disappear. In this paper, the perturbation theory of complex Weierstrass canonical form for regular matrix pencils is investigated. By using matrix pencil theory and the Weierstrass canonical form of the pencil we obtain bounds for the finite elementary divisors of a perturbed pencil. Moreover we study robust stability of a class of linear matrix difference equations (of first and higher order) whose coefficients are square constant matrices.     

A robust robust optimization result

We study the loss in objective value when an inaccurate objective is optimized instead of the true one, and show that “on average” this loss is very small, for an arbitrary compact feasible region.     

Intelligent active force control of a 3-RRR parallel manipulator incorporating fuzzy resolved acceleration control

This paper introduces a novel intelligent control scheme for robust and precise positioning and orientation of a class of highly non-linear 3-RRR (revolute-revolute-revolute) planar parallel manipulator. The primary objective is to force the manipulator to track accurately a prescribed Cartesian trajectory when the system is subjected to different types of disturbances in the forms of forced harmonic excitations. A two level fuzzy tuning resolved acceleration control (FLRAC) is first designed and implemented to the system to demonstrate the stable response of the manipulator in performing trajectory tracking tasks in the absence of the disturbances. In this scheme, the first level of fuzzy tuning is used to acquire the proportional-derivative (PD) gains linearly while the second level considers non-linear tuning for determining the other parameters of the fuzzy controller to increase its performance. Then, the controller is added in series with an active force controller (AFC) to create a novel two degree-of-freedom (DOF) controller known as FLRAC-AFC which is subsequently and rigorously tested for system robustness and accuracy in tracking the prescribed trajectory. The simulation study provides further insight into the potentials of the proposed robotic system in rejecting the disturbances for the given operating conditions. The results clearly show that the FLRAC-AFC scheme provides a much superior trajectory tracking capability compared to the conventional linear RAC alone.     

Copositive optimization - Recent developments and applications

Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile field of research. It is a special case of conic optimization, which consists of minimizing a linear function over a cone subject to linear constraints. The diversity of copositive formulations in different domains of optimization is impressive, since problem classes both in the continuous and discrete world, as well as both deterministic and stochastic models are covered. Copositivity appears in local and global optimality conditions for quadratic optimization, but can also yield tighter bounds for NP-hard combinatorial optimization problems. Here some of the recent success stories are told, along with principles, algorithms and applications.     

Selection of a representative value function in robust multiple criteria ranking and choice

We introduce the concept of a representative value function in robust ordinal regression applied to multiple criteria ranking and choice problems. The proposed method can be seen as a new interactive UTA-like procedure, which extends the UTA^GMS and GRIP methods. The preference information supplied by the decision maker (DM) is composed of a partial preorder and intensities of preference on a subset of reference alternatives. Robust ordinal regression builds a set of general additive value functions which are compatible with the preference information, and returns two binary preference relations: necessary and possible. They identify recommendations which are compatible with all or at least one compatible value function, respectively. In this paper, we propose a general framework for selection of a representative value function from among the set of compatibles ones. There are a few targets which build on results of robust ordinal regression, and could be attained by a representative value function. In general, according to the interactively elicited preferences of the DM, the representative value function may emphasize the advantage of some alternatives over the others when all compatible value functions acknowledge this advantage, or reduce the ambiguity in the advantage of some alternatives over the others when some compatible value functions acknowledge an advantage and other ones acknowledge a disadvantage. The basic procedure is refined by few extensions. They enable emphasizing the advantage of alternatives that could be considered as potential best options, accounting for intensities of preference, or obtaining a desired type of the marginal value functions.