Matrix Inequality Constraints Research Articles

An Anti-Windup Method Based on an LADRC for Miniaturized Inertial Stabilized Platforms on Unmanned Vehicles in Marine Applications

This paper investigates an anticipatory activation anti-windup approach based on Linear Active Disturbance Rejection Control (LADRC) to address the influences of accelerated saturation on the actuators in a Miniaturized Inertial Stabilized Platform (MISP) with extreme external disturbance. The proposed method aims to eliminate the high-frequency vibrations on the Line of Sight (LOS) of electro-optical devices during actuator saturation. To achieve this, the Linear Extended State Observer (LESO) is modified by adding saturation feedback to the total disturbance observed state variable, which is operated as an anticipatory activation anti-windup compensator. The stability of the proposed controller is discussed, and the gains are optimized by the Linear Matrix Inequality (LMI) constraints though quadratic programming and an H-infinite performance indicator. Additionally, as the multiple activated scheme for anti-windup, the effectiveness of immediate activation in dealing with accelerated saturation is compared and analyzed. These comparisons and verification are implemented through simulations, where the external disturbance is introduced using recorded attitude data from USV sailing. Finally, experiments are conducted on an MISP for a visual tracking system, demonstrating that the anticipatory activation mothed effectively suppresses high-frequency vibrations on the LOS during instances of accelerated saturation.

Asynchronous event-triggered guaranteed cost control of uncertain 2-D Markov jump Roesser systems with actuator saturation

This paper investigates the asynchronous event-triggered guaranteed cost control problem for two-dimensional Markov jump Roesser systems with parameter uncertainties and actuator saturation. The hidden Markov model is constructed to characterize the asynchronous phenomenon induced by the mode mismatch between the system and the controller, and a hidden Markov model-based event-triggered mechanism is adopted in controller design to save communication resources. The convex hull representation is employed to process saturated inputs. By using the quadratic Lyapunov function methods and linear matrix inequality techniques, some sufficient criteria are developed to guarantee the asymptotic stability of the addressed system with a guaranteed cost under three different boundary conditions. Finally, a convex optimization algorithm with linear matrix inequality constraints is proposed to design the optimal asynchronous event-triggered guaranteed cost controller, and a numerical example is considered to demonstrate its validity.

Piecewise non-linear model predictive control with bounded disturbance

This work addresses the problem of robust [Formula: see text] model predictive control for constrained piecewise non-linear systems corrupted by norm-bounded disturbances for the first time. In this approach, the system can have different operating points with different subregions. In each subregion, the system is made up of an affine model disturbed by an additive non-linear term that is locally Lipschitz. The employment of the piecewise non-linear model leads to a non-convex optimization problem, which is far more difficult to solve. It is also much more challenging to develop the [Formula: see text] model predictive control for piecewise non-linear systems. The proposed method introduces a control strategy in the form of a convex optimization problem subject to linear matrix inequality constraints, with the ability to minimize the L2 gain between the disturbance input and the controlled output. The proposed controller guarantees system stability with a prescribed [Formula: see text] disturbance attenuation level under switching between subregions. Simulations on a highly non-linear chemical process are conducted to demonstrate the efficacy of the proposed approach.

Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS

‘Co-design’ problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS).

Parameter Identification of Hydraulic Manipulators Considering Physical Feasibility and Control Stability

In the challenging applications of hydraulic robots, control performance in the full workspace is required for successful task completion. The model-based controller of the hydraulic manipulator is an effective means to improve control performance. However, most of the existing identification methods rely on least squares or weighted least squares, which may lead to the physically infeasible parameters. Although the physical feasibility of inertial parameters can be solved by the linear matrix inequality, physical feasibility and prior knowledge constraints of hydraulic parameters, such as bulk modulus and valve port coefficients, have not been considered in the identification process. Parameters that do not satisfy constraints will affect system stability in the model-based controller. In this paper, an identification framework is proposed, which integrates inertial, friction, hydraulic parameters physical feasibility. Compared with the non-identified parameters, the ratio of tracking error to maximum velocity with the proposed method is reduced by 50%-56%. Compared with the least squares identification, the control stability in the full workspace is guaranteed. The proposed method is applicable to serial hydraulic manipulators with arbitrary degrees of freedom and is supported by experimental analysis of a hydraulic manipulator.

Optimal non-fragile control design for linear systems under amplitude and rate saturation: An LMI approach

In this paper, the problem of optimal non-fragile guaranteed cost control design for linear systems subject to input amplitude and rate saturation is addressed. Sufficient conditions for the existence of a non-fragile state feedback are obtained by Lyapunov stability theory. The designed controller not only guarantees the asymptotic stability of the overall closed-loop system with a minimum upper bound of a cost function, but also ensures the actuator saturation avoidance. This problem is transformed into an optimization problem with linear matrix inequality (LMI) constraints. The proposed method guarantees that the control input amplitude and rate remain within the allowable ranges and do not exceed the considered bounds. The simulation results illustrate the effectiveness and superiority of the proposed theoretical results.

Event-Triggered Resilient Filtering With the Interval Type Uncertainty for Markov Jump Systems.

The problem of event-triggered resilient filtering for Markov jump systems is investigated in this article. The hidden Markov model is used to characterize asynchronous constraints between the filters and the systems. Gain uncertainties of the resilient filter are the interval type in this article, which is more accurate than the norm-bounded type to model the uncertain phenomenon. The number of linear matrix inequalities constraints can be decreased significantly by separating the vertices of the uncertain interval, so that the difficulty of calculation and calculation time can be reduced. Moreover, the event-triggered scheme is applied to depress the consumption of network resources. In order to find a balance between reducing bandwidth consumed and improving system performance, the threshold parameter is designed as a diagonal matrix in the event-triggered scheme. Utilizing the convex optimization method, the sufficient conditions are derived to guarantee that the filtering error systems are stochastically stable and satisfy the extended dissipation performance. Finally, a single-link robot arm system is delivered to certify the effectiveness and advantages of the proposed method.

Nearly Linear-Phase 2-D Recursive Digital Filters Design Using Balanced Realization Model Reduction

This paper presents a new method for the design of separable-denominator 2-D IIR filters with nearly linear phase in the passband. The design method is based on a balanced realization model reduction technique. The nearly linear-phase 2-D IIR filter is designed using 2-D model reduction from a linear-phase 2-D FIR filter, which serves as the initial filter. The structured controllability and observability Gramians Ps and Qs serve as the foundation for this technique. onal positive-definite matrices that satisfy 2-D Lyapunov equations. An efficient method is used to compute these Gramians by minimizing the traces of Ps and Qs under linear matrix inequality (LMI) constraints. The use of these Gramians ensures that the resulting 2-D IIR filter preserves stability and can be implemented using a separable-denominator 2-D filter with fewer coefficients than the original 2-D FIR filter. Numerical examples show that the proposed method compares favorably with existing techniques.

A co-design condition for dynamic event-triggered feedback linearization control

This paper presents a novel approach for dynamic event-triggered feedback linearization control of nonlinear systems. Two main aspects should be accounted for in this context: the internal perturbation induced by the sampling error and the stability of the internal dynamics. To deal with the first aspect, a trigger function is designed to cancel out the influence of the internal perturbation completely. Concerning the second one, a sufficient stability analysis condition is derived by representing the internal dynamics as a polytopic differential inclusion. These two ingredients allow for performing the co-design of dynamic event-triggered feedback linearization controllers. A multi-objective optimization problem with linear matrix inequality constraints is formulated to achieve the maximization of the estimate of the region of attraction and the minimization of the number of transmissions. Numerical examples illustrate the effectiveness of the proposed approach.

Frequency-based multivariable control design with stability margin constraints: A linear matrix inequality approach

In this paper, a proportional–integral–derivative controller design problem for stable multivariable process is considered. A frequency-based control technique is formulated as a convex optimization problem with linear matrix inequality constraint. The multivariable proportional–integral–derivative controller is designed so that H∞ norm of the difference between the designed loop gain function and a desired one is minimized. Linear matrix inequality constraints on the stability margin guarantees designed loop stability. Process frequency domain data is used to solve the proposed optimization problem. Knowledge of the process parametric model is not necessary. The desired loop gain transfer function is defined from the reference complementary sensitivity function. Simulation results show the comparison between the proposed technique and technique from the literature. In these examples, the proposed technique resulted in stable closed-loops different from the others and in a reduction of the performance indices.

Robust fault-tolerant control of a class of uncertain nonlinear switched systems with actuator saturation

This paper addresses the robust fault-tolerant control problem for a class of uncertain nonlinear switched systems with actuator saturation. Our aim is to design a switching law and a robust fault-tolerant control law for guaranteeing that the closed-loop system is asymptotically stabilizable, while at the same time the attraction domain estimation is as large as possible. By using the multiple Lyapunov functions method, sufficient conditions for robust fault-tolerant stabilisation are proposed for the closed-loop system. Then, when some scalar parameters are given in advance, the problem of fault-tolerant controller design and attraction domain estimation is transformed into a convex optimisation problem with linear matrix inequality (LMI) constraints. Finally the validity of the proposed design method is verified by a numerical example.

State estimation strategy for a class of nonlinear algebro-differential parameter-varying systems

This paper deals with the state estimation problem for nonlinear algebro-differential parameter-varying systems. Sufficient conditions for the existence of the observer which guarantee stability regarding Linear Matrix Inequalities constraints using the Lyapunov stability theory are given. The approach presented includes the proportional and proportional-integral observer as particular cases and allows some robustness concerning uncertainties and modelling errors and its steady state accuracy. A rolling disc model is given to illustrate our results.

Total power deficit estimation for isolated power system network using H∞ norm method

An isolated electrical network with an independent local distributed generator is very sensitive towards the contingencies between load demand and supply. Although the network system has less complexity in term of structure, its stability condition is crucial due to its stand-alone operating condition. Hence, to monitor the stability of the network, total power deficit is the only variable that can be estimated. This study proposed to utilize the filtering problem to design an estimator that can estimate the total power deficiency. For verification, the design estimator was tested under two cases which are nominal case and parameter uncertainty case. In nominal case, the system parameters are assumed to be known while in parameter uncertainty case the system has contaminated with uncertain parameter where its admissible value is laying in a given polytope. With complying the linear matrix inequality (LMI) constraint, the main objective function of the norm was guaranteed with minimum upper bound. The results show that the dynamical behaviors of designed estimator successfully trace the actual power deficit signal at steady state with minimal estimation error.

Stochastic robust predictive fault-tolerant control for discrete systems with actuator faults

Abstract A stochastic robust predictive fault-tolerant control approach is proposed for a class of industrial processes with uncertainties, external disturbances and the random failure of actuators. First, a process model of the above system is established in terms of state space. It is further converted into a new augmented form containing the state deviation and output tracking error. By means of the augmented model, the designed control law is given. Then the related theorem and corollary in the form of linear matrix inequality constraints are provided for solving the gain of the control law under different probabilities of failure. Under a certain probability, the occurrence of a failure is regarded as a switching condition. Conventional control is adopted when the failure does not occur, while fault-tolerant control is performed when the failure occurs. Finally, a pressure holding phase case is provided for verifying the feasibility of the given approach.

Virtual reference feedback tuning for linear discrete-time systems with robust stability guarantees based on set membership

In this paper we propose a novel methodology that allows us to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant reference signals. The approach uses both (i) virtual reference feedback tuning for enforcing suitable performance and (ii) the set membership framework for providing a-priori robust stability guarantees. Indeed, an uncertainty set for the system parameters is obtained through set membership identification, where an algorithm based on the scenario approach is proposed to estimate the inflation parameter in a probabilistic way. Based on this set, robust stability conditions are enforced as linear matrix inequality constraints within an optimization problem whose linear cost function relies on virtual reference feedback tuning. To show the generality and effectiveness of our approach, we apply it to two of the most widely used yet simple control schemes, i.e., where tracking is achieved thanks to (i) a static feedforward action and (ii) an integrator in closed-loop.The proposed method is not direct due to the set membership identification. However, the uncertainty set is used with the objective of providing robust stability guarantees for the closed-loop system and it is not used for the definition of the cost function, which instead is based on data. The effectiveness of the method is shown with reference to three simulation examples. A comparison with other data-driven methods is carried out.

Robust Max-Min Fairness Transmission Design for IRS-Aided Wireless Network Considering User Location Uncertainty

In this paper, we propose a robust max-min fairness transmission design for intelligent reflecting surface (IRS)-aided wireless network in the presence of user location uncertainty. In particular, the non-isotropic reflection property for the IRS element is considered. We investigate the joint design of the active transmit beamformer at the base station (BS) and the passive phase shift matrix along with the deployment orientation (facing/pointing direction) of the IRS for maximizing the worst-case minimum signal-to-interference-plus-noise ratio (SINR) received by the users. In order to show the potential gains obtained by adjusting the deployment orientation of the IRS, a single-input-single-output (SISO) system is studied where a closed-form signal-to-noise ratio (SNR) of the user is obtained. For the multi-user case, to solve the resulting non-convex problem, an inexact-alternating-optimization algorithm consisting of a double-loop iteration is proposed. Specifically, in the inner loop, an optimization problem with semi-infinite constraints needs to be solved to increase the worst-case min-SINR compared to the given SINR reference value. We first transform the semi-infinite constraints into linear matrix inequality (LMI) constraints with finite form by applying the Taylor expansion approximation method, the general S-procedure, and the general sign-definiteness lemma. Then an efficient alternating optimization (AO) algorithm based on the two-dimensional search method, negative square penalty (NSP) method, and successive convex approximation (SCA) technique is proposed. While in the outer loop, we update the given SINR reference value as the worst-case minimum SINR obtained after each inner loop iteration. The whole algorithm terminates when the updated SINR reference values converge. Simulation results demonstrate the effectiveness of the proposed algorithm, and also show the additional system performance gain brought by the optimization of the IRS deployment orientation compared to its counterpart with fixed IRS deployment orientation, especially for a smaller IRS element number and a more prominent non-isotropic reflection property of the IRS element.

Reduced-order model based dynamic tracking for soft manipulators: Data-driven LPV modeling, control design and experimental results

We propose a generic nonlinear reduced-order tracking control method for elastic soft robots. To this end, a new linear parameter varying (LPV) control framework is developed using the data collected from the soft robots. Specifically, for LPV modeling we first derive a nonlinear robot model, which is large-scale by nature, using finite element methods (FEM). Then, a proper orthogonal decomposition (POD) algorithm is used to generate a set of linearized reduced-order models, representing the local behaviors of the soft robot at different operating points within the workspace. Via a unified POD projector, not only the order of these linearized models can be significantly reduced but also their mechanical structure and stability properties can be preserved for LPV modeling and control design. Next, using radial basis function (RBF) networks, we propose an iterative training method to build the LPV robot model by interpolating a subset of selected linearized models with a specified interpolation error. For LPV control design, the equivalent-input-disturbance (EID) concept is exploited to develop a dynamic tracking control scheme, which is composed of three core components: feedforward control, disturbance-estimator control and feedback control. The feedforward control is designed to account for the effects of the trajectory reference and the time-varying affine term, issued from the FEM-based model linearization. The disturbance-estimator control is obtained from a generalized proportional integral LPV observer, which also provides the estimated reduced-order states for feedback control. The observer-based feedback control design is reformulated as a convex optimization problem under linear matrix inequality (LMI) constraints. The globally uniformly ℓ∞ stability of the closed-loop LPV robot model is guaranteed by means of Lyapunov stability theory. Experimental tests are conducted with a soft Trunk robot, inspired by the elephant trunk, under several scenarios with small and large deformations to show the effectiveness of the proposed LPV tracking control framework. A comparative study is also performed with a recent linear EID-based controller and an iterative learning controller to emphasize the interests this nonlinear control method for soft elastic robots. This paper is complemented with a series of demonstration videos: https://bit.ly/3D8C4Vd.

Attitude control for a full-scale flexible electric solar wind sail spacecraft on heliocentric and displaced non-Keplerian orbits

The electric solar wind sail (E-sail) spacecraft is a fuel-free propulsion system with promising potential in deep space explorations and solar activity monitoring missions. It is challenging to conduct attitude control for a full-scale flexible E-sail spacecraft due to its complex dynamical characteristics, including the spatial multi-scale, high-speed spinning, and large deformations. In this work, a double-loop attitude control strategy for the flexible E-sail spacecraft with high accuracy and efficiency is proposed. The E-sail spacecraft is firstly modeled by the referenced nodal coordinate formulation, where the rotations are described by the Lie group approach. A state-feedback controller developed from the Lyapunov stability theory is prescribed as the inner loop. The gain is obtained by solving a semidefinite programming problem with linear matrix inequality constraints, which is globally optimal and numerically reliable. A multi-variable proportional-integral-derivative controller is then introduced as the outer loop for flexibly enhancing the control performance. Several missions of the E-sail spacecraft, including attitude maneuvers on heliocentric and displaced non-Keplerian orbits, are studied to show that the desired attitude adjustments are accurately and efficiently achieved without exciting high-frequency oscillations. The double-loop control strategy has great prospects in designing and implementing orbital transformation and long-term stable Sun-orbiting missions.

Dual-Mode Robust Fuzzy Model Predictive Control of Time-Varying Delayed Uncertain Nonlinear Systems With Perturbations

For time-varying delayed nonlinear systems with parameter uncertainties and persistent disturbances, an online and an offline robust fuzzy model predictive control (RFMPC) algorithms are proposed in this paper. Both methods guarantee the input-to-state stability (ISS) of the system. Furthermore, a novel alternative optimization (AOP) approach and a dual-mode OP/AOP strategy are proposed to prevent the performance deterioration of the online optimal control (OP) approach due to the challenges in addressing the bilinear matrix inequality (BMI) constraints. With the established AOP and dual-mode OP/AOP techniques, the optimization problem constrained by BMIs is transformed into convex, and a significantly more precise approximation of the ellipsoidal minimal robust positively invariant (EmRPI) set can be calculated. Besides, the system can eventually converge into a more compact ellipsoidal set. These two alternative optimization methods can be easily extended to various nonlinear systems. A numerical example and a continuous-time stirring tank (CSTR) example are provided to validate the effectiveness and advantages of the established methodologies.

Dissipativity-based conditions for the feedback stabilization of systems with time-varying input delays

This note is concerned with presenting new dissipativity-based conditions for the stabilizability of discrete-time systems with time-varying delays by linear static output feedback (SOF). We demonstrate that the feasibility of nonlinear matrix inequalities for the design of feedback stabilizing gains derived from the literature is equivalent to the feasibility of a linear matrix inequality establishing dissipativity of the system plus one matrix inequality constraint. An iterative strategy allowing the computation of stabilizing SOF gains is then developed based on a new relaxed sufficient condition. Compared with other popular approaches in the literature, such as the celebrated cone complementarity linearization (CCL) method, the strategy avoids providing initial “guesses” for the matrix variables, which is especially complicated when dealing with a large number of matrices. Due to being a particular case of SOF with an identity output matrix, static state feedback (SSF) gains can also trivially be computed by exploiting the developed conditions.