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This paper presents an optimization-based perspective for incorporating disturbance decoupling constraints into controller synthesis, which paves the way for utilizing numerical optimization tools. We consider the constraints arising from the following sets of static state feedback: (i) The set of all disturbance decoupling controllers; (ii) The set of all disturbance decoupling and stabilizing controllers. To inner approximate these sets by means of matrix equations or inequalities, we provide a unifying review of the relevant results of the geometric control theory. The approximations build on the characterization of controlled invariant subspaces in terms of the solvability of a linear matrix equation (LME) involving the state feedback. The set (i) is inner approximated through the LME associated with any element of an upper semilattice generated by controlled invariant subspaces. The set (ii) is inner approximated through a bilinear matrix inequality (BMI) and the LME associated with any element of a different upper semilattice generated by internally stabilizable controlled invariant subspaces. However, the resulting inner approximations depend on the subspaces chosen from the semilattices. It is shown that a specific (internally stabilizable) self-bounded controlled invariant subspace, which is the best choice regarding eigenvalue assignment, yields the largest inner approximation for both of the sets among (internally stabilizable) self-bounded controlled invariant subspaces. The inner approximations exactly characterize the controller sets under particular structural conditions. We have been driven by two primary motivations in investigating inner approximations for the sets above: (i) Enable the formulation of a variety of equality (and inequality) constrained optimization problems, where cost functions, such as a norm of the state feedback, can be minimized over a large subset of the set of all disturbance decoupling (and stabilizing) controllers; (ii) Introduce the disturbance decoupling constraints to members of the control systems community who might not be quite familiar with the elegant geometric state-space theory, similar to the authors themselves. This can add another dimension to research endeavors in resilient control of networked multi-agent systems. [ABSTRACT FROM AUTHOR]

As we move to increasingly complex cyber–physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler–Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in 4. 5 ms while respecting workspace constraints and switching between a 'left' and 'right' bend in the elbow joint. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a topology optimization method considering fatigue constraints for the jacket support structure of offshore wind turbine. Jacket support structure is an important component and supports the whole wind turbine weight under the dynamic environmental loads, which would induce serious fatigue problems. To obtain the optimal structural layout, the topology optimization method considering fatigue constrained is introduced for the jacket support structure under the dynamic load. The fatigue lifetime is constrained base on the Miner's cumulative damage rule. The design sensitivity of the objective and constraint functions are evaluated analytically, while the equivalent static load approach is applied. Some typical topology optimization problems are introduced to verify the effectiveness of the proposed method, and this method can obtain the appropriate layouts with stable convergence. A case study on the OC4 reference jacket indicates that the method can achieve a reasonable layout structure under the dynamic load, which meets the fatigue constraint. And the final design is reconstructed based on the topology optimization layout. Finally, a lighter jacket structure has good performance on the ultimate bearing capacity, eigenfrequency, and buckling, which is suited for long operation life. [ABSTRACT FROM AUTHOR]

The cooperation of multi-agent systems (MAS) based on distributed model predictive control (DMPC) is a current research hotspot, and how to more effectively handle additive disturbances and reduce resource consumption are two difficult problems that need to be solved. In view of this, this paper aims to design a more effective DMPC strategy for MAS, so as to effectively deal with the above problems without loss of the control performance. Firstly, a finite-horizon constrained optimization problem is established for MAS, in which a robustness constraint is designed to effectively handle additive disturbances. Then, a new efficient event-triggering condition is designed, which is established by considering the mixed information of differential and integral of the state error. Furthermore, based on the dual-mode control, an event-triggered robust DMPC algorithm is proposed to further reduce the resource consumption of the system. In addition, theoretical results are provided through analysis and deduction to ensure the iterative feasibility of the algorithm, stability of the closed-loop system and Zeno-free behavior. Finally, the proposed algorithm is applied to two examples for simulation and comparison to verify its effectiveness. The simulation results show that compared to DMPC and classical event-triggered DMPC methods, the proposed algorithm can reduce the average resource consumption of MAS by more than 81% and 36%, respectively, which indicates that the proposed strategy can effectively reduce the computation and communication burden of MAS without affecting the control performance. [ABSTRACT FROM AUTHOR]