Asymptotic stability, ℓ2 gain, boundness analysis, and control synthesis for switched systems: a switching frequency approach

This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.

Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay

This paper considers the control synthesis problem and its solution using symbolic regression. Symbolic regression methods, which were previously called genetic programming methods, allow one to use a computer to find not only the parameters of a given regression function but also its structure. Unlike other works on solving the control synthesis problem using symbolic regression, the novelty of this paper is that for the first time this work employs a training dataset to address the problem of general control synthesis. Initially, the optimal control problem is solved from each point in a given set of initial states, resulting in a collection of control functions expressed as functions of time. A reference model is then integrated into the control object model, which generates optimal motion trajectories using the derived optimal control functions. The control synthesis problem is framed as an approximation task for all optimal trajectories, where the control function is sought as a function of the deviation of the object from the specified terminal state. The optimization criterion for solving the synthesis problem is the accuracy of the object’s movement along the optimal trajectory. The paper includes an example of solving the control synthesis problem for a mobile robot using a supervised machine learning method. A relatively new method of symbolic regression, the method of variational complete binary genetic programming, is studied and proposed for the solution of the control synthesis problem.

The paper is concerned with a problem of adaptive tracking system control synthesis. It is assumed that a nonlinear object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that a nonlinear state feedback plus parameter adaptation are able to ensure its asymptotic stability. The proposed controller design is based on modified adaptive backstepping method. In this approach, as opposite to the standard backstepping, the design process has been reduced to a single iteration, which enables avoiding complicated recursive procedure. An extra task here is to find a control synthesis of linear-like, chained system. The solution of the last problem in general framework is also presented. The obtained thereby controller has several attractive features of both the feedback linearization and backstepping schemes.

An identification control is a control of an object which mathematical model is unknown. For such objects initially the problem of identification is solved, and then for the resulting object model the problem of control synthesis is solved. As a result of control synthesis we obtain a multi-dimensional function that describes the dependence of control on the object state. After the implementation of this function in the control unit of the real object, it achieves the goal of control with optimal value of the quality criteria. To solve the identification and synthesis problems we use the method of network operator, which with the help of evolutionary algorithms finds the structure and parameters of the functions describing the model and functional dependence of control from the object state. In this paper, an example of using a network operator to solve the problem of identification control synthesis for a multilink robot is given.

This work eonsiden the H, norm control of structural systems with collocated sensors and actuators using an analytical upper bound approach. A parametrization of the output feedback control gains that achieve a desired H, norm bound is obtained using an analytical solution of the Bounded Real Lemma. This approach is verified experimentally on a cantilevered aluminum beam with two collocated pairs of piezoceramic patches that serve as sensors and actuators. The finite element model of this beam is developed and the simulations show a drop of -6 dB in the H, norm of the closed loop system. Experimental results verify the simulated results and demonstrate the effectiveness of this method. The proposed control methodology has obvious computational advantages compared to traditional H, control design methods, especially for lnrge scale systems. The control of structural systems with collocated sensors and actuators has been shown to provide great advantages from a stability, passivity, robustness and an implementation viewpoint. For example, collocated control can easily be achieved in a space structure when an attitude rate sensor is placed at the same point as a torque actuator.(l)(2) The actuator placement and sizing optimization for vibration sup pression of a collocated beam structure is discussed in Ref. (3).Collocation of sensors and actuators leads to symmetric transfer functions. Several other classes of engineering sys- tems, such as circuit systems, chemical reactors and power networks, can be modelled as systems with symmetric trans- fer functions. Stabilization, robustness, model reduction and control of such systems has been examined recently.(4)(5) The H, norm control of structural systems has attracted a lot of attention recently due to the interpretation of the H, norm in the frequency domain. In early work, D-K iteration method was used to design H, controllers for a non-collocated flexible shucture. Now state space H, control based on the standard Riccati equation approach or the linear matrix inequality (LMI) formulation is a well developed control synthesis tool. The optimal static state feedback and full-order dynamic output feedback H, con- trol synthesis problems can be solved using iterations on the corresponding Riccati solutions or via the computational solution of a convex LMI optimization problem.(7)(8) On the other hand, the static output feedback and the fixed-order dynamic output feedback H, control synthesis problems are difficult computational problems since they require the

The article is devoted to solving the problem of controlling a system defined by ordinary differential equations with a nonlinear right-hand side, which has the property of quasi-monotonicity with respect to off-diagonal elements. The equations also contain control parameters and uncertainties (errors), the possible values of which should satisfy some point-wise restrictions. The problem of control over a finite time interval is considered in order to transfer the state of the system to a given target set. The current state of the system is unknown, and for the formation of a control strategy, only a priori estimates of the initial state are available, as well as the results of incomplete and inaccurate measurement results received online. To solve the problem, a well-known general scheme is used, according to which it is necessary to consistently solve three subtasks: the approximate construction of information sets of the system, solvability sets, and, finally, the control synthesis problem. In this paper, this general scheme is successfully implemented for the special class of nonlinear systems under consideration. Theorems on external interval estimates of information sets, internal estimates of solvability sets, as well as on sufficient conditions for the solvability of the control problem are proved. Formulas for feedback control are obtained, depending on the so-called generalized position, formed on the basis of available information about the system and measurement results. The possibility of applying the theoretical results obtained to solve specific control problems is confirmed by the model example analyzed in the work.

Automated Synthesis of Fixed Structure QFT Controller using Interval Constraint Satisfaction Techniques

In this work, we consider a simplified version of the distributed control synthesis problem where the system is modeled as a Boolean network and specifications are given as propositional formulae on environment and system variables. In this relatively static Boolean setting, (centralized) reactive control synthesis problem reduces to a quantified Boolean satisfiability problem which can be solved by off-the-shelf SAT solvers. For the distributed control synthesis, we propose a recursive algorithm that starts from a global assume-guarantee specification and maps it to local assume-guarantee specifications for individual subsystems. Finding these local assume- guarantee specifications leads to a modular design framework. For instance, local controllers for subsystems can be synthesized independently via SAT or a local subsystem can be replaced with another subsystem that satisfies the same local assume-guarantee specifications. We also investigate how the interconnection structure of the network affects the performance of this algorithm. In particular, we show that if the interconnection structure is a multi-tree and the global assumptions and guarantees satisfy certain independence conditions, the algorithm is complete.

This paper carries out an analysis of the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gain and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance for singular linear systems under actuator saturation. The notion of bounded state stability (BSS) with respect to the influence of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> disturbances is introduced and conditions under which a system is bounded state stable are established in terms of linear matrix inequalities (LMIs). The disturbance tolerance capability of the system is then measured as the bound on the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> norm of the disturbances under which the system remains bounded state stable and the disturbance rejection capability is measured by the restricted L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gain from the disturbance to the system output or L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> norm of the system output. Based on the BSS conditions, the assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as LMI constrained optimization problems. By viewing the feedback gain as an additional variable, these optimization problems can be readily adapted for control design. Our analysis and design reduce to the existing results for regular linear systems in the degenerate case where the singular linear system reduces to a regular system, and to the existing results for singular systems in the absence of actuator saturation or when the disturbance is weak enough to not cause saturation.

Robust controller synthesis attracts reviving research interest, driven by\nthe rise of learning-based systems where uncertainty and perturbation are\nubiquitous. Facing an uncertain situation, a robustly stabilizing controller\nshould maintain stability while operating under a perturbed system deviating\nfrom its nominal specification. There have been numerous results for robust\ncontroller synthesis in multiple forms and with various goals, including\nmu-synthesis, robust primal-dual Youla, robust input-output, and robust system\nlevel parameterizations. However, their connections with one another are not\nclear, and we lack a general approach to robust controller analysis and\nsynthesis.\n To serve this purpose, we derive robust stability conditions for general\nsystems and formulate the general robust controller synthesis problem. The\nconditions hinge on the realization-stability lemma, a recent analysis tool\nthat unifies existing controller synthesis methods. Not only can the conditions\ninfer a wide range of existing robust results, but they also lead to easier\nderivations of new ones. Together, we demonstrate the effectiveness of the\nconditions and provide a unified approach to robust controller analysis and\nsynthesis.\n

This study considers the problem of control synthesis via static output feedback for time‐delay systems with restricted frequency domain specifications. A static output‐feedback (SOF) controller is designed by a two‐stage method. The first stage is to design an initial full‐information (FI) controller, and the second stage is to explore an SOF controller heuristically from the initial FI controller. An iterative algorithm to optimise the initial FI controller is constructed. Moreover, a more effective algorithm to explore an SOF controller is also formulated. Finally, the effectiveness of the proposed method is illustrated via the classical ACC benchmark problem of cart‐spring system.

The paper is concerned with the problem of adaptive tracking system control synthesis. It is assumed that a nonlinear, feedback linearizable object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that proportional state feedback plus parameter adaptation are able to assure its asymptotic stability. This form of controller permits online compensation of unknown model nonlinearities and exogenous disturbances, which results in satisfactory tracking performance. An interesting feature of the system is that the whole process control is performed without requisite asymptotic convergence of approximator parameters to the postulated ‘true’ values. It has been noticed that the parameters play rather a role of slack variables on which potential errors (that otherwise would affect the state variables) cumulate. The system's performance has been tested via Matlab/Simulink simulations via an example of ship path‐following problem. Copyright © 2009 John Wiley &amp; Sons, Ltd.

The problem of optimal control synthesis of complex nonlinear and multidimensional systems oriented on the building of integrated control systems with the adaptation and self-organization properties is of much current interest. The development of optimization methods employed in control problems demonstrated their effectiveness and has led to the construction of algorithms of approximate solution of optimization problems that significantly extends the class of control problems that can be set. In this work we consider a synthesis of optimal control for affine nonlinear system, in which a special emphasis is placed on the degenerate problems of optimal control. Our approach is based on the extension of the method of minimization of generalized work function by properly transforming the initial nondegenerate problem of optimal control into degenerate problem of optimal control synthesis. The search for the solution is based on the suboptimal strategy that includes the construction of minimizing sequences that converge interval-wise to the optimal solution of the initial problem. We obtain some optimality conditions as well as the necessary and sufficient conditions of existence of optimal solution.

Given a Markov decision process (MDP) and a linear-time ($ømega$-regular or Linear Temporal Logic) specification which reasons about the infinite-trace behavior of a system, the controller synthesis problem aims to compute the optimal policy that satisfies said specification. Recently, problems that reason over the complementary infinite-frequency behavior of systems have been proposed through the lens of steady-state planning or steady-state policy synthesis. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior of the agent. We present an algorithm to find a deterministic policy satisfying $ømega$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.