State Feedback Controller Design Research Articles

Meta-heuristic optimization-based robust [formula omitted] controller design for active suspension systems subject to actuator saturation

This study focuses on designing robust H∞ controllers to mitigate actuator saturation-related issues of active suspension systems. Two design methods are presented: one utilizing full-state feedback and the other relying on measurable output feedback. The H∞ state-feedback control incorporates actuator saturation directly into the design, representing the control input with the saturation function in the state-space model. The resulting optimization-based design problem, derived from theoretical stability analyses, poses a non-convex NP-hard problem under bilinear matrix inequality (BMI) constraints. To address this challenge, the study proposes a meta-heuristic optimization-based technique, providing a straightforward yet effective method to manage the BMI problem. The scope extends to practical implementation considerations, where suspension systems may only utilize measurable output variables. The H∞ static output-feedback control case is explored by extending the design of a full-order state-feedback controller. Despite the BMI-related challenges entailed in this scenario, the proposed meta-heuristic optimization-based design technique demonstrates flexibility in managing BMI conditions, thus eliminating the need to modify the controller design methodology. A noteworthy contribution of this study is its consistent application of the same meta-heuristic optimization-based technique for designing both H∞ state-feedback and static output-feedback controllers. Experimental results validate the effectiveness of the proposed robust H∞ control strategies.

Policy gradient methods for designing dynamic output feedback controllers

This paper proposes model-based and model-free policy gradient methods (PGMs) for designing dynamic output feedback controllers for discrete-time partially observable deterministic systems without noise. To fulfill this objective, we first show that any dynamic output feedback controller design is equivalent to a state-feedback controller design for a newly introduced system whose internal state is a finite-length input–output history (IOH). Next, based on this equivalence, we propose a model-based PGM and show its global linear convergence by proving that the Polyak–Łojasiewicz inequality holds for a reachability-based lossless projection of the IOH dynamics. Moreover, we propose a model-free implementation of the PGM with a sample complexity analysis. Finally, the effectiveness of the model-based and model-free PGMs is investigated through numerical simulations.

Adaptive state feedback controller design for efficient biodiesel production under kinetic uncertainty

In this study, we optimize the quality and economic performance of biodiesel production through a scenario-based adaptive state feedback control framework. Our goal is to maximize the operational efficiency while ensuring the production of on-spec biodiesel, despite uncertainties in reaction kinetics. A first-principle model is employed to describe the process dynamics, with kinetic parameters estimated online using a moving horizon estimator (MHE). A pool of state feedback controllers is created via off-line nonlinear optimization and metaheuristic algorithm based on sampled kinetic scenarios. Then, the uncertainty space is partitioned into several clusters, each linked to an optimal controller from the pool. During online operation, the appropriate controller is selected by matching the estimated kinetic parameters to the corresponding cluster. Simulation studies on a semi-batch reactor demonstrate that manipulating the methanol feed flow rate and heat duty with our control approach significantly improves operational efficiency, reduces online computational time, and enhances robustness to kinetic uncertainties compared to model predictive control (MPC).

State-Feedback and Nonsmooth Controller Design for Truck Platoon Subject to Uncertainties and Disturbances

Intelligent truck platoons can benefit road transportation due to the short gap and better fuel economy, but they are also subject to dynamic uncertainties and external disturbances. Therefore, this paper develops a novel robust control algorithm for connected truck platoons. By introducing a linearized expression method of platoon error dynamics based on state measurement, the state feedback mechanism combined with a nonsmooth controller for a truck platoon is proposed in the development of the distributed control method. The state-feedback controller can drive the nominal platoon system to the state of second-order consensus, and the nonsmooth controller counterparts the uncertainties and disturbances. The convergence and string stability of the proposed control algorithm are demonstrated both theoretically and experimentally, and the effectiveness and robustness are also verified by simulation tests.

Observer-based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay.

This article introduces an observer-based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time-varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose-insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer-based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer-based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed-loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

Distributed quantized secure bipartite consensus of linear multi‐agent systems with switching topologies and sequential scaling attacks

AbstractThis paper considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced.

Robust control with protected feedback information for switched systems under injection attacks

In this paper, the robust security protection control for switched systems is studied. A robust anti-disturbance mechanism using the Radial Basis Function Neural Network (RBFNN) is proposed for switched systems, which can approximate and compensate for the impact of unknown disturbance on the system state. Then, a network security protection mechanism based on encoder and decoder is presented, which has the ability to resist the dual impact on the feedback information caused by the network privacy snooping and data injection attacks. Accordingly, stability analysis and state-feedback controller design are given for the switched systems under unknown disturbance, network privacy snooping and injection attacks. Finally, simulation results illustrate the effectiveness of the proposed method.

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

This paper investigates state feedback control for a class of discrete-time multiple input and multiple output nonlinear systems from the perspective of model-free adaptive control and state observation. The design of a dynamic state feedback control can be efficiently carried out using dynamic linearization and state observation. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation tests and experimentation on a continuous stirred tank reactor are carried out to validate the effectiveness of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The growth in the scale of factories and the complexity of associated production processes increases the complexity and time involved in associated mathematical modelling. Data driven approaches to control remove the need to model processes. To the best of the authors’ knowledge, existing approaches to model-free adaptive control (MFAC) of general systems are all based on an input-output control paradigm. These methods thus cannot guarantee the stability of the system state. The purpose of this study is to develop a novel Model-Free Adaptive Control (MFAC) approach to achieve control of the system state. In this paper, the assumptions required to achieve model-free adaptive control by state feedback are presented mathematically. A controller design and the associated stability proof are then presented. Numerical simulation and experimentation is conducted to validate the effectiveness of the proposed approach. In future research, state feedback data control in the presence of random disturbances will be investigated.

Quantized feedback control of distributed radar system with packet dropouts and time-varying delays described by 2D system

In this paper, we present quantized state feedback control for the distributed radar with packet dropouts and time-varying delays. The measurements of state signal are quantized by logarithmic quantizer before being communicated. The measurements missing and time delay often occur due to the communication channel failure. The data missing phenomena was modeled by a Bernoulli distributed stochastic variable taking values of 1 and 0, the delays are time-varying. Firstly, the quantized state feedback control design is transformed into stability analysis for a 2D stochastic system. Secondly, we obtain the stability condition based on linear matrix inequality (LMI) of mean-square asymptotic stability of the 2D stochastic system. Additionally, a quantized state feedback controller is designed based on the linear matrix inequality theorem to meet the environmental requirements of the distributed radar system. Compared to existing methods, the proposed controller designed under this method demonstrates robustness and stability in addressing the three challenges of packet loss, time-varying delays, and quantization errors in the distributed radar. Finally, the effectiveness of the proposed method is validated through the simulation example.

An LMI-based robust state-feedback controller design for the position control of a knee rehabilitation exoskeleton robot: Comparative analysis

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

H∞ control of switched Lurie systems with dwell time

This article deals with the [Formula: see text] control problems of switched Lurie systems. Our purpose is to design switching signals and state feedback controllers with time-varying control gains that make the closed-loop switched Lurie systems absolutely stable. Based on switched time-varying Lyapunov–Lurie function, time-varying controllers corresponding to two kinds of switching signals are proposed. On this basis, the control synthesis conditions are given. It is worth mentioning that our results can deal with the situation that all subsystems are not stabilizable. Finally, the obtained results are applied to a flexible joint robotic arm model with switchings of parameter values. Another simulation example of switched Lurie systems is considered to illustrate the validity of the presented approaches.

Design of an Event-Triggered State Feedback Control for Fractional-Order Interconnected Systems

Design of an Event-Triggered State Feedback Control for Fractional-Order Interconnected Systems

Robust H∞ observer-based model predictive controller for uncertain linear discrete-time systems due to external disturbances

This article investigates an observer-based robust model predictive control (RMPC) design to control the uncertain discrete-time linear systems with disturbances. To make a more practical scheme, it is supposed that the uncertain system has been faced with unknown disturbance and input constraints. The proposed RMPC approach is based on a state feedback control design that ensures the [Formula: see text] performance criterion to attenuate disturbance affections. Furthermore, in view of practical application, the control law is constructed based on the estimated states obtained from the Luenberger observer. Based on Lyapunov’s theory, the input to state practically stability (ISPS) of the closed-loop system is ensured. Appropriate conditions for the ISPS of the closed-loop system and the estimation error are obtained in terms of online linear matrix inequalities (LMIs) which lead to obtaining the time-varying gain matrices of both controller and observer. Finally, to validate the obtained results, the proposed approach is applied to a numerical example and it is compared with the existing control scheme and the superiority is proved.

The dependent coordinates in the linearization of constrained multibody systems: Handling and elimination

In this paper, the handling of the dependent coordinates in the linearization of constrained multibody systems is clarified. To this end, a brief but comprehensive overview of linearization approaches used in the field of Multibody System Dynamics is presented. These procedures are illustrated by using a common notation and classified into four groups, depending on the initial form of the nonlinear equations of motion and the selection of the generalized coordinates (a redundant or a minimal set). The handling of the dependent coordinates in each of the procedures is discussed. The linearized equations of motion of constrained multibody systems are of great importance in several applications, such as linear stability and modal analyses, the design of linear state feedback controllers or the building of state and input estimators, like Kalman filters. When modeling a constrained multibody system, a number of coordinates greater than the number of degrees of freedom of the system is usually used. While some linearization approaches make use of the complete set of coordinates, several procedures are based on a coordinate partition in terms of independent and dependent coordinates to reduce the number of linearized equations of motion. In this latter scenario, the role of the dependent coordinates in the linearization is important and, in a general case, these dependent coordinates cannot be ignored to obtain the correct linearized equations of motion. This aspect, which may seem obvious, is not straightforward and is addressed in this work. The importance of considering the set of dependent coordinates in the linearization is demonstrated with a well-acknowledged bicycle benchmark multibody model and an electric kickscooter multibody model with rear and front suspensions. To this end, the Jacobian matrix and the linear stability results of these case studies are computed by considering different choices of independent and dependent coordinates.

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

Air Levitation State Feedback Control Using Pole Placement and Kalman Filter

State feedback controller design and implementation of Kalman filter for Air levitation system is studied in simulation environment (Matlab/Simulink) and on real laboratory plant, low cost Floatshield device developed recently at our University and having an open source support, Takács (2022). Nonlinear model and its linearized state space representation are used for a pole placement controller design. The main focus is on Kalman filter implementation via its equations, which can help better understanding of its principle. Simulation results received for linear and nonlinear systems are compared with real plant experiments. The authors believe that the presented control design topics and corresponding tasks can contribute to developing students’ skills in control design and further enhance educational potential of hands-on laboratories using low cost air levitation device.

State-Feedback Control Design for Polynomial Discrete-Time Systems obtained via Second-Order Runge-Kutta Discretization

This paper addresses the state-feedback control problem for the class of state-polynomial discrete-time systems. The continuous-time polynomial nonlinear model is discretized by the second-order Runge-Kutta method. The Lyapunov theory and the exponential stability were employed to derive the conditions. The sum of squares formulation was used to check the constraints. Two approaches are presented, the first makes use of the Lyapunov function to recover the gain matrices. While the second formulation allows the design of rational state feedback control gains. We evaluated the impact of the step size used in the discretization process in the results. Numerical experiments were used to illustrate the potential of the proposed technique.

A new Takagi-Sugeno fuzzy system approach for fuzzy state feedback controller design and its application to malware propagation on heterogeneous complex network

Abstract— Nowadays, digital transformation has brought many great changes and is becoming an essential part of real life, however, it also goes along with a considerable likelihood of being targeted in cyberattack. Indeed, the more businesses embrace digital transformation or use online services, the more opportunities hackers have to expand their cyberattacks. Hence, there is an essential need on analyzing and predicting of cyberattack on network systems. For this aim, we propose to study a controlled fractional network-based SCIRS (Susceptible - Carrier - Infectious - Recovered - Susceptible) malware propagation model and its stabilization problem based on fractional interconnected Takagi-Sugeno fuzzy system. A fuzzy state feedback controller is proposed to asymptotically stabilize the unstable malware-free equilibrium of the proposed malware propagation model and then, we establish sufficient conditions in terms of linear matrix inequalities. The effectiveness of proposed approach is illustrated by a case study of SCIRS malware propagation model on heterogeneous complex network.

On the State-Feedback Controller Design for Polynomial Linear Parameter-Varying Systems with Pole Placement within Linear Matrix Inequality Regions

The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main contribution of this paper, the controller is designed by considering the time-varying parameter rate as a tuning parameter with a continuous control gain in such a way that the closed-loop eigenvalues lie in a complex plane subset, with high-order time-varying parameters defining the system dynamics. Simulation results are presented, aiming to show the effectiveness of the proposed controller design.