Gain-Scheduling Controller Synthesis for Networked Systems with Full Block Scalings

This work presents a framework to synthesize structured gain-scheduled controllers for structured plants that are affected by time-varying parametric scheduling blocks. Using a so-called lifting approach, we are able to handle several structured gain-scheduling problems arising from a nested inner and outer loop configuration with partial or full dependence on the scheduling block. Our resulting design conditions are formulated in terms of convex linear matrix inequalities and permit to handle multiple performance objectives.Comment: 16 pages, 4 figure

Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that guarantees the tracking performance of the algorithm. Two variants of this algorithm are investigated. The first one can be used to solve nonlinear programming problems while the second variant is aimed to treat online parametric nonlinear programming problems. The local convergence of these variants is proved. An application to a large-scale benchmark problem that originates from nonlinear model predictive control of a hydro power plant is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure

Co-Design of Time-Invariant Dynamical Systems

Design of a physical system and its controller has significant ramifications on the overall system performance. The traditional approach of first optimizing the physical design and then the controller may lead to sub-optimal solutions. This is due to the interdependence between the physical design and control parameters through the dynamic equations. Recognition of this fact paved the way for investigation into the ``Co-Design" research theme wherein the overall system's physical design and control are simultaneously optimized. Co-design involves simultaneous optimization of the design and the control variables with respect to certain structural property as constraint. The structural property may be in the form of stability, observability or controllability leading to different types of co-design problems. Co-design optimization problems are non-convex optimization problems involving bilinear matrix inequality (BMI) constraints and are NP-hard in general. In this dissertation, four interrelated research tasks in the area of co-design are undertaken. In the first research task, a theoretical and computational framework is developed to co-design a class of linear time invariant (LTI) dynamical systems. A novel solution procedure based on an iterative combination of generalized Benders decomposition and gradient projection method is developed guaranteeing convergence to a solution in a finite number of iterations which is within a tolerance bound from the nearest local/global minimum. In the second research task, the sparse and structured static feedback design problem is modeled as a co-design problem. A formulation based on the alternating direction method of multipliers is used to solve the sparse feedback design problem which has given robustness as a constraint. In the third research task, the optimal actuator placement problem is formulated as a co-design problem. The actuator positions are modeled as $0/1-$binary design variables and result in a mixed integer nonlinear programming (MINLP) problem. In the fourth research task, a heuristic procedure to place sensors and design observer is developed for a class of Lipschitz nonlinear systems. The procedure is based on the relation between Lipschitz constant, sensor locations and observer gain. The vast and diverse application potential of co-design across all engineering branches is the primary motivation and relevance of the research work carried out in this dissertation

Networked Realization of Discrete-Time Controllers

We study the problem of mapping discrete-time linear controllers into potentially higher order linear controllers with predefined structural constraints. Our work has been motivated by the Wireless Control Network (WCN) architecture, where the network itself behaves as a distributed, structured dynamical compensator. We make connections to model reduction theory to derive a method for the controller embedding based on minimization of the H∞-norm of the error system. This allows us to frame the problem as synthesis of optimal structured linear controllers, which enables the utilization of design-time iterative procedures for systems’ approximation. Finally, we illustrate the use of the mapping procedure by embedding PID controllers into the WCN substrate, and show how to reduce the computation overhead of the approximation procedure

Sufficient Dilated LMI Conditions for Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems

New sufficient dilated linear matrix inequality (LMI) conditions for the ∞ static output feedback control problem of linear continuous-time systems with no uncertainty are proposed. The used technique easily and successfully extends to systems with polytopic uncertainties, by means of parameter-dependent Lyapunov functions (PDLFs). In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with even more relaxed structure are employed. It is shown that these slack variables provide additional flexibility to the solution. It is also shown, in this paper, that the proposed dilated LMI-based conditions always encompass the standard LMI-based ones. Numerical examples are given to illustrate the merits of the proposed method

Dissipative State and Output Estimation of Systems with General Delays

Dissipative state and output estimation for continuous time-delay systems pose a significant challenge when an unlimited number of pointwise and general distributed delays (DDs) are concerned. We propose an effective solution to this open problem using the Krasovski\u{\i} functional (KF) framework in conjunction with a quadratic supply rate function, where both the plant and the estimator can accommodate an unlimited number of pointwise and general DDs. All DDs can contain an unlimited number of square-integrable kernel functions, which are treated by an equivalent decomposition-approximation scheme. This novel approach allows for the factorization or approximation of any kernel function without introducing conservatism, and facilitates the construction of a complete-type KF with integral kernels that can encompass any number of differentiable (weak derivatives) and linearly independent functions. Our proposed solution is expressed as convex semidefinite programs presented in two theorems along with an iterative algorithm, which eliminates the need of nonlinear solvers. We demonstrate the effectiveness of our method using two challenging numerical experiments, including a system stabilized by a non-smooth controller.Comment: submitting to TA

Optimal control with structure constraints and its application to the design of passive mechanical systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Page 214 blank.Includes bibliographical references.Structured control (static output feedback, reduced-order control, and decentralized feedback) is one of the most important open problems in control theory and practice. In this thesis, various techniques for synthesis of structured controllers are surveyed and investigated, including H2 optimization, H[infinity] optimization, L1 control, eigenvalue and eigenstructure treatment, and multiobjective control. Unstructured control-full- state feedback and full-order control-is also discussed. Riccati-based synthesis, linear matrix inequalities (LMI), homotopy methods, gradient- and subgradientbased optimization are used. Some new algorithms and extensions are proposed, such as a subgradient-based method to maximize the minimal damping with structured feedback, a multiplier method for structured optimal H2 control with pole regional placement, and the LMI-based H2/H[infinity]/pole suboptimal synthesis with static output feedback. Recent advances in related areas are comprehensively surveyed and future research directions are suggested. In this thesis we cast the parameter optimization of passive mechanical systems as a decentralized control problem in state space, so that we can apply various decentralized control techniques to the parameter design which might be very hard traditionally. More practical constraints for mechanical system design are considered; for example, the parameters are restricted to be nonnegative, symmetric, or within some physically-achievable ranges. Marginally statable systems and hysterically damped systems are also discussed. Numerical examples and experimental results are given to illustrate the successful application of decentralized control techniques to the design of passive mechanical systems, such as multi-degree-of-freedom tuned-mass dampers, passive vehicle suspensions, and others.by Lei Zuo.S.M