Linear Inequality Constraints Research Articles

Robust State Feedback Control with D-Admissible Assurance for Uncertain Discrete Singular Systems

This study addresses the state feedback control associated with D-admissible assurance for discrete singular systems subjected to parameter uncertainties in both the difference term and system matrices. Firstly, a refined analysis criterion of D-admissible assurance is presented, where the distinct form embraces multiple slack matrices and has lessened linear matrix inequalities (LMIs) constraints, which may be beneficial for reducing the conservatism of admissibility analysis. In consequence, by hiring the state feedback control, controller design issues with pole locations, which directly dominate the system performance, are mainly treated. For all the presented criteria can be formulated by the strict LMIs, they are thus suitably solved via current LMI solvers to conduct a state feedback controller with specific poles’ locations of system’s performance requirements. Finally, two numerical examples illustrate that the presented results are efficient and practicable.

Exponential qubit reduction in optimization for financial transaction settlement

We extend the qubit-efficient encoding presented in (Tan et al. in Quantum 5:454, 2021) and apply it to instances of the financial transaction settlement problem constructed from data provided by a regulated financial exchange. Our methods are directly applicable to any QUBO problem with linear inequality constraints. Our extension of previously proposed methods consists of a simplification in varying the number of qubits used to encode correlations as well as a new class of variational circuits which incorporate symmetries thereby reducing sampling overhead, improving numerical stability and recovering the expression of the cost objective as a Hermitian observable. We also propose optimality-preserving methods to reduce variance in real-world data and substitute continuous slack variables. We benchmark our methods against standard QAOA for problems consisting of 16 transactions and obtain competitive results. Our newly proposed variational ansatz performs best overall. We demonstrate tackling problems with 128 transactions on real quantum hardware, exceeding previous results bounded by NISQ hardware by almost two orders of magnitude.

Non‐fragile reliable guaranteed cost control and L2‐gain analysis for saturated switched nonlinear systems

AbstractFor the nonlinear continuous‐time saturated switched system, this article investigates the problem of non‐fragile reliable guaranteed cost control of the system. Due to the simultaneous occurrence of controller perturbation, actuator saturation and actuator failure, when designing the cost function, this article considers three scenarios affecting the system performance, controller perturbation, actuator saturation and actuator failure, simultaneously in the cost function, which has not been investigated in the existing literature. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization of non‐fragile reliable guaranteed cost control and the performance index. In order to ensure the exponential stabilization of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and the non‐fragile reliable guaranteed cost state feedback controllers are designed by using the minimum dwell‐time method. Furthermore, by solving optimization problems with linear matrix inequality constraints, the minimum upper bound of the cost function and the performance of the system are determined. At the end of the article, we give a numerical example to verify the effectiveness of the proposed approach.

Robust predictive fault-tolerant control under actuator random failures

A robust predictive fault-tolerant switching control method is presented for a class of industrial processes that are prone to random actuator failures. The primary contribution is the combination of stochastic control theory with robust predictive control to represent the occurrence of system failure in the form of probability, thus significantly enhancing the conventional fault-tolerant control approach. First, a state-space model of the system is established, which is then transformed into an enhanced form that includes state deviations and output tracking errors. This augmented model enables the formulation of fault-tolerant switching control laws with fault probabilities, ensuring system convergence and tracking capabilities. Subsequently, linear matrix inequality constraints are given to find the switching controller gains under recovery and fault probabilities. Under certain probabilities, failure triggers fault-tolerant control, while recovery prompts a shift back to conventional control. Final, we validate the feasibility of our approach with a case study involving pressure regulation.

A switched system approach to exponential stabilization of interval type-2 fuzzy nonlinear systems with packet dropouts

This paper investigates the exponential stabilization problem for interval type-2 (IT2) fuzzy system with parameter uncertainties and packet dropouts. The sample-and-hold characteristic is simulated by employing an input delay methodology, and we present a model for the packet dropout phenomenon using switched approach. Some novel two-side delay-dependent looped-functionals are proposed by considering state information in the intervals from tr to t and t to tr+1 which relaxes the monotonic constraint of the Lyapunov–Krasovskii functional (LKF) and enhances the utilization of the actual sampling pattern. Additionally, some free-weighting matrices, slack matrices, the bound information in membership functions (MFs) and the signs of the first-order time derivative of fuzzy MFs are used to obtain a novel relaxed sufficient conditions for exponential stabilization of interval type-2 fuzzy systems (IT2 FS). Based on the LKF theory, new relaxed sufficient conditions with linear matrix inequalities (LMIs) constraints are derived. According to the criterion, sampled-data controller is devised to ensure that the closed-loop system is exponential stabilization. Finally, an illustrative example is presented to demonstrate the practicality and effectiveness of the method proposed. Comparative analysis highlights the simplicity and practicality of the suggested algorithm.

Sampling-Based Global Path Planning Using Convex Polytope Approximation for Narrow Collision-Free Space of Humanoid

In this paper, we propose a computationally fast method of sampling-based global path planning for humanoids under Manifold Constraints such as closed kinematic chains and Volume-Reducing Constraints such as collision avoidance. In multi-contact and whole-body manipulation of humanoids, narrow collision-free space causes path planning to take a long computation time (narrow corridor problem). In previous research of constrained planning, Manifold Constraints are locally approximated by tangent plane, and steering motions along Manifold Constraints are found efficiently by projection or continuation methods. In this paper, we applied constrained planning algorithms to collision avoidance. Since tangent plane cannot approximate Volume-Reducing Constraints, we adopted convex polytope instead of tangent plane. Both Manifold Constraints and Volume-Reducing Constraints are locally approximated by convex polytope with linear equality and inequality constraints, and steering motions inside the convex polytope are found efficiently by the SQP-based prioritized inverse kinematics. We developed CP-KPIECE (Convex Polytope approximation-based KPIECE) with this approach. Benchmarks using the humanoid JAXON proved the effectiveness of our approach for fast path planning in narrow collision-free space of humanoids.

Relevant interval perturbation method for uncertainty analysis of structural–acoustic coupling model

The parameters in structural–acoustic coupling models are often coupled with each other, and the independence of the uncertain parameters is a necessary condition for using the traditional interval perturbation method. This article proposes a relevant interval perturbation method for the uncertainty analysis of a structural–acoustic coupling model with uncertain-but-bounded parameters. Aiming at the linear inequality constraint relationship in the uncertain parameters, this method introduces a sensitivity ranking mechanism for the uncertainty parameters, which overcomes the limitation of uncertain parameter independence in the traditional interval model, and effectively restrains the interval expansion phenomenon of the system response in the uncertainty analysis. Through numerical examples, it is demonstrated that the relevant interval perturbation analysis method can effectively solve a constrained problem when there are uncertain parameters, and the obtained response interval radius is smaller than that of the traditional method under constraint conditions.

A strategy based on integer programming for optimal dosing and timing of preventive hypoglycemic treatments in type 1 diabetes management

Background and objectivesOne of the major problems related to type 1 diabetes (T1D) management is hypoglycemia, a condition characterized by low blood glucose levels and responsible for reduced quality of life and increased mortality. Fast-acting carbohydrates, also known as hypoglycemic treatments (HT), can counteract this event. In the literature, dosage and timing of HT are usually based on heuristic rules. In the present work, we propose an algorithm for mitigating hypoglycemia by suggesting preventive HT consumption, with dosages and timing determined by solving an optimization problem. MethodsBy leveraging integer programming and linear inequality constraints, the algorithm can bind the amount of suggested carbohydrates to standardized quantities (i.e., those available in “off-the-shelf” HT) and the minimal distance between consecutive suggestions (to reduce the nuisance for patients). ResultsThe proposed method was tested in silico and compared with competitor algorithms using the UVa/Padova T1D simulator. At the cost of a slight increase of HT consumed per day, the proposed algorithm produces the lowest median and interquartile range of the time spent in hypoglycemia, with a statistically significant improvement over most competitor algorithms. Also, the average number of hypoglycemic events per day is reduced to 0 in median. ConclusionsThanks to its positive performances and reduced computational burden, the proposed algorithm could be a candidate tool for integration in a DSS aimed at improving T1D management.

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.

Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.

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.

Distributed continuous-time optimization for convex problems with coupling linear inequality constraints

Distributed continuous-time optimization for convex problems with coupling linear inequality constraints

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).

A model-based hypothesis framework to define and estimate the diel niche via the 'Diel.Niche' R package.

How animals use the diel period (24-h light-dark cycle) is of fundamental importance to understand their niche. While ecological and evolutionary literature abound with discussion of diel phenotypes (e.g. diurnal, nocturnal, crepuscular, cathemeral), they lack clear and explicit quantitative definitions. As such, inference can be confounded when evaluating hypotheses of animal diel niche switching or plasticity across studies because researchers may be operating under different definitions of diel phenotypes. We propose quantitative definitions of diel phenotypes using four alternative hypothesis sets (maximizing, traditional, general and selection) aimed at achieving different objectives. Each hypothesis set is composed of mutually exclusive hypotheses defined based on the activity probabilities in the three fundamental periods of light availability (twilight, daytime and night-time). We develop a Bayesian modelling framework that compares diel phenotype hypotheses using Bayes factors and estimates model parameters using a multinomial model with linear inequality constraints. Model comparison, parameter estimation and visualizing results can be done in the Diel.Niche R package. A simplified R Shiny web application is also available. We provide extensive simulation results to guide researchers on the power to discriminate among hypotheses for a range of sample sizes (10-1280). We also work through several examples of using data to make inferences on diel activity, and include online vignettes on how to use the Diel.Niche package. We demonstrate how our modelling framework complements other analyses, such as circular kernel density estimators and animal movement modelling. Our aim is to encourage standardization of the language of diel activity and bridge conceptual frameworks and hypotheses in diel research with data and models. Lastly, we hope more research focuses on the ecological and conservation importance of understanding how animals use diel time.

Distributed Optimisation With Linear Equality and Inequality Constraints Using PDMM

Distributed Optimisation With Linear Equality and Inequality Constraints Using PDMM

Distributed Nash Equilibrium Seeking for Multicluster Aggregative Game of Euler-Lagrange Systems With Coupled Constraints.

This article considers the distributed Nash equilibrium seeking problem of a multicluster aggregative game subject to local set constraints, consensus constraints in the same cluster, and coupled linear equality and nonlinear inequality constraints among all clusters. In the considered game, each cluster is composed of a group of players formulated by uncertain Euler-Lagrange (EL) dynamics, and its objective is to minimize its own cost function, which is the sum of the local functions of all players in the cluster. The local cost function of each player depends on its own decision and an aggregate of the decisions of all the players. An adaptive continuous-time distributed strategy is developed for uncertain EL systems to reach the generalized Nash equilibrium (GNE) of multicluster aggregative game. In particular, a new auxiliary system is synthesized using a projection operator, gradient descent, and dynamic average consensus to estimate the GNE. Based on the outputs of the auxiliary system, an adaptive tracking algorithm is developed for an EL system with uncertain parameters. Using the Lyapunov stability theory, it is shown that the developed distributed strategy achieves accurate convergence to the GNE. Finally, a numerical example is presented to demonstrate the theoretical results.

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.