Linear Matrix Inequality Optimization Problem Research Articles

Minimal operation region prediction for networked control robotic manipulators subject to time‐varying delays and disturbances

AbstractDue to the disturbances and varying latency, a teleoperated robotic manipulator might not comply with the master control commands. Although prior studies on minimising the impact of network latency and disturbances on teleoperated robots were conducted, there has been very little research on the prediction of minimal operation regions of robotic arms, especially in the worst‐case scenarios when the disturbances and time delays still prevail even after impact minimisation. This study investigates the problem and proposes a novel solution to predicting minimal operation regions of networked control robotic manipulators. The proposed method can be used to forecast safe operation regions in which the manipulators will certainly enter and exclude regions that the robots will never penetrate. Leveraging on a Lyanonov Krasovskii criterion, the method performs region prediction by establishing minimal reachable bounding sets of the nonlinear, perturbed robotic arm's state vectors guided via a time‐varying delay‐dominant network. Though predominantly nonlinear, the entire prediction process is formulated as a tractable Linear Matrix Inequality (LMI) optimisation problem, which can be solved efficiently and effectively. Efficacy of the proposed method is validated with simulations where a simulated robotic arm is distorted with time‐varying delays and disturbances.

A linear matrix inequality approach to optimal reset control design for a class of nonlinear systems

AbstractIn this article, the problem of the optimal reset control design for Lipschitz nonlinear systems is addressed. The reset controller includes a base linear controller and a reset law that enforces resets to the controller states. The reset law design is strongly dependent on the appropriate design of the base controller. For this reason, in this article, the base controller and reset law are simultaneously designed. More precisely, an optimal dynamic output feedback is considered as the base controller which minimizes the upper bound of a quadratic performance index, and a reset law is used to improve the transient response of the closed‐loop system. This design is done in a full offline procedure. The problem is transformed into a set of linear matrix inequalities (LMIs), and the reset controller is obtained by solving an offline LMI optimization problem. Finally, two examples are presented to illustrate the effectiveness and validity of the proposed method.

Learning Human Behavior in Shared Control: Adaptive Inverse Differential Game Approach.

To enhance the collaborative intelligence of a machine, it is important for the machine to understand what behavior a human may adopt to interact with the machine when performing a task in shared control. In this study, an online behavior learning method is proposed for continuous-time linear human-in-the-loop shared control systems by using the system state data only. A two-player nonzero-sum linear quadratic dynamic game paradigm is used for modeling the control interaction between a human operator and an automation that actively compensates for human control action. In this game model, the cost function representing the human behavior is assumed to have an unknown weighting matrix. Here, we want to learn the human behavior or retrieve the weighting matrix by using the system state data only. Accordingly, a new adaptive inverse differential game (IDG) method, which integrates concurrent learning (CL) and linear matrix inequality (LMI) optimization, is proposed. First, a CL-based adaptive law and an interactive controller of the automation are developed to estimate the feedback gain matrix of the human online, and second, an LMI optimization problem is solved to determine the weighting matrix of the human cost function. Finally, simulation results on a cooperative shared control driver assistance system are provided to elucidate the feasibility of the developed method.

Human-in-the-Loop Behavior Modeling via an Integral Concurrent Adaptive Inverse Reinforcement Learning.

One goal of artificial intelligence (AI) research is to teach machines how to learn from humans, such that they can perform a certain task in a natural human-like way. In this article, an online adaptive inverse reinforcement learning (IRL) approach to human behavior modeling is proposed to enhance machine intelligence for a class of linear human-in-the-loop (HiTL) systems using the state data only, where the human behavior is described by a linear quadratic optimal control model with an unknown weighting matrix for the quadratic cost function. First, an integral concurrent adaptive law is developed to learn the human feedback gain matrix online using the demonstrated state data only, which removes the persistent excitation (PE) conditions required by traditional adaptive estimation approaches and thus is more in line with real applications. Then, with the learned feedback gain matrix, the IRL problem is formulated as a linear matrix inequality (LMI) optimization problem, which can be efficiently solved to retrieve the weighting matrix of the human cost function. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.

Distributed Adaptive Inverse Differential Game Approach to Leader's Behavior Learning for Multiple Autonomous Followers

In this study, the leader's behavior learning problem is investigated for a class of leader-follower systems, where the leader's behavior is assumed not a priori known to all followers that are autonomous. A multi-player nonzero-sum differential game is introduced to indicate the control interaction between agents, where the leader's behavior is modelled by an unknown cost function. The autonomous followers aim to retrieve the weighting matrix in the leader's cost function collaboratively. A distributed online adaptive inverse differential game (IDG) approach to the leader's behavior learning is proposed for the autonomous followers. Specifically, a concurrent learning (CL) based adaptive law and an interactive game controller are first developed for each autonomous follower to learn the leader's feedback gain matrix online, while the feedback Nash equilibrium of the game can be achieved. Then, a linear matrix inequality (LMI) optimization problem is formulated to determine the weighting matrix of the leader's cost function for each autonomous follower. The proposed method simply requires that all followers share their interactive feedback gain matrices, not their private intents, and use only the system state data, not both the system state data and the leader's control input data. The main advantages of the proposed method are that it can be implemented online without requiring the persistent excitation condition and needs less computational power for all followers. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the developed method.

Finite-Time Control of Markov Jump Lur'e Systems With Singular Perturbations

This paper investigates the asynchronous controller design issue for Markov jump Lur'e systems with singular perturbations within a fixed time interval. For broader practical applications, the variation of system modes is regulated by a switched nonhomogeneous Markov process that corresponded to both lower-level nonhomogeneous stochastic jumping and higher-level deterministic switching. By resorting to the hidden nonhomogeneous-Markov model, an asynchronous control law that relies on the detected mode information is proposed. In light of the mode-dependent average dwell time strategy and mode-dependent stochastic system theory, the singularly perturbed parameter-independent conditions are attained to ensure the stochastic finite-time boundedness of the resulting systems. With respect to a linear matrix inequality optimization problem, a solution to the maximum singular perturbation parameter is obtained. Finally, the feasibility and applicability of the devised theoretical results are verified by simulation examples.

An iterative output feedback controller-design strategy for energy-to-peak structural vibration control

ABSTRACT To address the issue of inadequate control effect resulting from the challenge of measuring state feedback information comprehensively, this paper proposes an iterative output feedback energy-to-peak control method that solely depends on partial external observation data. This paper presents the computational steps for achieving a suboptimal solution to the output feedback bilinear matrix inequality constrained problem using an iterative linear matrix inequality approach. The proposed method overcomes the challenge of numerically solving the optimization problem. The unknown variables in the output feedback linear matrix inequality optimization problem are transformed equivalently to obtain a new linear matrix inequality optimization problem. The numerical results of the two optimization problems are then used to iterate with each other and obtain a suboptimal solution. A comprehensive analysis was conducted on an 8-story building structure, utilizing state feedback, output feedback, and iterative output feedback energy-to-peak control techniques. The results of the study indicate that the proposed iterative output feedback energy-to-peak control approach efficiently reduces the displacement and acceleration response of the structure, exhibiting superior control effectiveness than both the state feedback and output feedback energy-to-peak control methods. The findings demonstrate the practicality and versatility of the suggested method.

Robust Model Predictive Control for Two-DOF Flexible-Joint Manipulator System

This paper presents a practical study on how to improve the ℋ∞ performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon ℋ∞ controller is designed to improve the system ℋ∞ performance while still satisfying the input–output constraints of the uncertain system. First, the uncertain controlled system model of the two-DOF FJMS is established via the Lagrange equation method, Spong’s assumption, and the linear fractional transformation (LFT) technique. Then, the control requirements and input–output constraints of the uncertain system are transformed into the linear matrix inequality (LMI) via the theory of ℋ∞ control and the full-block multiplier technique. Next, the LMI optimization problem refreshed by the current state is addressed at each sample moment with the idea of the moving-horizon control of the model predictive control (MPC), and the calculated gain is implemented to the nonlinear closed-loop system under the state feedback structure. The validity and feasibility of the designed control scheme is finally verified via the results of simulation experiments.

Integrated fire/flight control coupler design for armed helicopters based on improved non-monotone adaptive trust region algorithm with distributionally robust optimization

Aiming at enhancing the extent of military automatization and the effectiveness of armed helicopters in complex battlefield environment, integrated fire/flight control (IFFC) coupler connects the fire control system and the flight control system which is used to generate the optimal flight command signals. However, it is difficult to obtain satisfactory flight command signals within a certain firing accuracy due to the unavoidable uncertain information in battlefield environment. In this paper, a new IFFC scheme is proposed for armed helicopters against complex combat by using the idea of distributionally robust optimization combined with the framework of trust region. Initially, a vector equation and coordinate transformation are employed to acquire the relative motion model of the IFFC coupler problem in complex battlefield environment. Moreover, an improved performance index is designed according to the constraints, and the original non-convex problem is handled by the Taylor formula combined with an improved BFGS (Broyden–Fletcher–Goldfard–Shanno) algorithm. Considering the uncertain parameters during optimization, the non-linear distributionally robust optimization is transformed into a linear matrix inequality optimization problem based on the worst-case conditional value-at-risk (WC-CVaR) approximation. Then, an algorithmic framework with a non-monotone adaptive trust region algorithm is given to obtain the optimal flight command signals. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

Composite adaptive online inverse optimal control approach to human behavior learning

There have been broad ranges of human-in-the-loop (HiTL) control systems, like fly-by-wire aircraft, share driving, and energy management. To develop advanced HiTL control systems with augmented intelligence, it is desirable that the machine is empowered to understand how a skilled human operator determines the control actions. It is common to model the human operator as an optimal controller with an unknown weighting matrix which depicts the tradeoff between multiple control objectives. Our aim is thus to learn the weighting matrix of the human objective function using only the system state measurement. Accordingly, for the HiTL system, a composite adaptive inverse optimal control (IOC) approach, which integrates concurrent learning (CL) based composite adaptive estimation and linear matrix inequality (LMI) optimization techniques, is proposed to learn human behavior online. The proposed composite adaptive IOC method consists of two steps: first, a composite adaptive update law is proposed to online estimate the human feedback gain matrix, which removes the persistent excitation condition required by traditional adaptive estimation methods, and then, an LMI optimization problem is solved to retrieve the weighting matrix of the human objective function with the learned feedback gain. The applicability and effectiveness of the proposed method are demonstrated with a steering control simulation.

Adaptive fuzzy observer based non-quadratic control for nonlinear system subject to actuator faults and saturation

This paper provides a new non-quadratic stabilization conditions based on adaptive fuzzy observer for a class of Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and both actuator faults and saturation. Firstly, an observer based fault tolerant control (FTC) is proposed, not only to estimate both system states and actuator faults but also to compensate for the actuator faults and to stabilize the faulty system with input constraints. The saturation effect is transformed into dead-zone nonlinearity and the generalized sector bound condition is used to estimate the attraction domain. To less the conservatism of the quadratic Lyapunov technique, a proper integral structure based on the non-quadratic function is investigated. The H∞ criteria is considered and the robust stabilization conditions of the faulty closed-loop system are expressed as a linear matrix inequalities (LMIs) optimization problem. Finally, the robustness and the advantages of the proposed approach are demonstrated through a mixed CSTR and a numerical example.

Distributed dynamic event-triggered communication and control for multi-agent consensus: A hybrid system approach

This paper investigates the output-based event-triggered communication and control for linear multi-agent consensus under a directed graph based on a co-design method. The communication among the agents, as well as the controller updates, are determined by some new event-triggering mechanisms, in order to reduce the use of the network resources. To simultaneously guarantee the significant properties including the asymptotic consensus, and strong Zeno-freeness (strictly positive inter-event times), a novel distributed dynamic event-triggered protocol is proposed. Unlike the most-existing emulation-based approaches in which the control gain is previously decided, a systematic co-design procedure is proposed to design the controller gain, the observer gain, and the event-triggering mechanisms altogether in terms of solving a linear matrix inequality optimization problem. Based on the resulting hybrid system framework, a hybrid model is established for the distributed closed-loop system and the asymptotic consensus is achieved. Finally, a numerical example is presented to verify our systematic design methodology.

Online Learning Human Behavior for a Class of Human-in-the-Loop Systems via Adaptive Inverse Optimal Control

To enhance the machines’ intelligence, it is important for them to learn how humans perform tasks. In this article, the issue of online adaptive learning human behavior is addressed for a class of human-in-the-loop (HiTL) systems using the state measurement only. The hypothesis underlying our study is that human behavior can be described by a linear quadratic optimal control model with an unknown weighting matrix for the quadratic cost function. In this model, the weighting matrix depicts the human tradeoff of various objectives. Our aim is thus to only use the system state measurement for learning the weighting matrix under the condition that human feedback gain matrix is unknown. A novel adaptive inverse optimal control approach to online learning human behavior is proposed for the HiTL system, which integrates adaptive estimation and linear matrix inequality (LMI) optimization techniques. Our approach consists of two steps: First, an adaptive law is developed to learn the human feedback gain matrix online using the system state measurement only, and second, the weighting matrix of human cost function is retrieved by solving an LMI optimization problem with the learned feedback gain matrix. Finally, simulation and experiment results on a steering assist system of intelligent vehicles are presented to illustrate the effectiveness of the proposed method.

Predictive control of uncertain systems over networks with redundant link

Networked systems using redundant channels to transmit data can effectively reduce the probability of data loss and improve system reliability and control margin. However, the structural complexity and economic cost of the system are also increased. To balance the redundancy and feasibility, the ratio of attraction domain to packet loss rate is defined as a balanced feasibility index. In this paper, single-channel packet loss is considered as Bernoulli distribution and a bounded packet loss network system control model is constructed as the arbitrary bounded packet loss control problem for redundant channel transmission network system. Therefore, the robust conditions of the closed-loop system and the constraints of the input and state are established under the framework of robust predictive control to construct the linear matrix inequality (LMI) optimization problem. Finally, to verify the effectiveness of the design method proposed in this paper, the discrete time-varying linear system and the main steam control system with redundant channels are used as study cases.

Robust H∞ Controller Design of Switched Delay Systems with Linear Fractional Perturbations by Synchronous Switching of Rule and Sampling Input

In this paper, we propose synchronous switching of rule and input to achieve H∞ performance for an uncertain switched delay system with linear fractional perturbations. Our developed simple scheme utilizes the linear matrix inequality optimization problem to provide a feasible solution for the proposed results; if the optimization problem was feasible, our proposed robust H∞ control could be designed. The feasibility of the optimization problem could be solved using the LMI toolbox of Matlab. In this paper, robust control with sampling is proposed to stabilize uncertain switching with interval time-varying delay and achieve H∞ performance. Interval time-varying delay and sampling were considered instead of constant delay and pointwise sampling. A full-matrix formulation approach is presented to improve the conservativeness of our proposed results. Some numerical examples are demonstrated to show our main contributions.

An iterative strategy for robust integration of fault estimation and fault-tolerant control

This paper considers fault estimation (FE) and fault-tolerant control (FTC) for linear parameter varying systems with actuator and sensor faults, uncertainties, and disturbances. The inevitable coupling between the FE and FTC functions needs to be taken into account in the design to ensure the overall FE-based FTC closed-loop system performance and robustness. This paper proposes an iterative strategy to achieve the robust integration of FE and FTC by leveraging the concepts of Separation Principle and Small Gain Theorem. The iterative algorithm involves solving multi-objective linear matrix inequality optimisation problems at each iteration and has finite-step convergence guarantee. Efficacy of the proposed algorithm and its advantages over the existing works are illustrated through numerical simulations.

Robust 1 observer design and circuit implementation for a class of faulty nonlinear systems

This paper presents a novel method to design a robust observer and its circuit implementation for the problems of fault diagnosis and state estimation in nonlinear systems expressed by Takagi–Sugeno models. The proposed observer is able to estimate states of system, process/actuator and sensor faults at the same time, and also has a high resistance to disturbances. The sufficient conditions to design the proposed observer such that ensuring the stability of the system based on to the Lyapunov theory and minimising an performance index are given by Linear Matrix Inequality (LMI) optimisation problems. Moreover, the circuit implementation of the Van der Pol system and the proposed observer scheme is provided in detail. Also, the simulation results validate the effectiveness of the proposed observer and fault diagnosis approach.

Sensor fault estimation for hydraulic servo actuator based on sliding mode observer

<abstract><p>In this paper, the mechanism for the fault estimation (FE) problem for a hydraulic servo actuator (HSA) with sensor faults is investigated. To deal with the design issues, we transformed the nonlinear model of HSA into a new coordinate system to estimate the sensor faults. In the new coordinate system, the Lipschitz conditions and system uncertainties are also considered. Then, we implement a sliding mode observer (SMO) approach to introduce the transformation scheme to make the system rational. The proposed fault estimation scheme essentially transforms the original system into two subsystems where the first one includes system uncertainties, but is free from sensor faults and the second one has sensor faults but without uncertainties. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating an $ H_\infty $ uncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribed $ H_\infty $ performance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Finally, the numerical example with simulation results is provided to validate the practicability and efficacy of the developed control strategy.</p></abstract>

Inverse optimal missile guidance law under constraints based on prescribed-time explicit reference governor

In this paper, the utilization of inverse-optimality-based prescribed-time explicit reference governor is investigated for missile intercepting against unknown maneuvering targets under performance and control input constraints. With an arctangent-based disturbance observer equipped for disturbance elimination, incorporating the inverse optimality approach into the missile interception guarantees the minimization of a performance index. In the framework of prescribed-time explicit reference governor, the control constraint is translated into a restriction of time-varying invariant set, and it follows the prescribed-time regulation of the applied reference along with the restriction satisfaction. The combined prescribed-time explicit reference governor approach could be transformed into a linear matrix inequality optimization problem, and its online solution over a receding horizon gives a Lyapunov function value for reference regulation and then control decisions in the continuous time. Simulation studies are performed to illustrate the performance of the proposed guidance control law.

Observer‐based control with enlarged domain of attraction for one‐sided Lipschitz systems subject to input saturation

AbstractThis article deals with the problem of observer‐based controller (OBC) design for a class of nonlinear systems in the presence of input saturation. The nonlinearities are assumed to satisfy the one‐sided Lipschitz and the quadratically inner‐bounded conditions. Sufficient conditions for the existence of OBC are derived by Lyapunov stability theory. The designed OBC not only ensures the asymptotic stability of the overall closed‐loop system with a domain of attraction as large as possible, but also guarantees the actuator saturation avoidance. This problem is converted into a linear matrix inequality optimization problem by judicious use of Young's relation for straightforward computation of the OBC gains. Finally, the effectiveness of the proposed design method is demonstrated by simulation results.