Additive Disturbances Research Articles

Robust Action Governor for Discrete-Time Piecewise Affine Systems With Additive Disturbances

In this letter, we introduce an extension of the Action Governor (AG), which is an add-on, supervisory scheme to a nominal control loop to enforce safety-related requirements. This extension enables AG design based on discrete-time piecewise affine (PWA) system models with additive set-bounded disturbance inputs and non-convex exclusion-zone avoidance constraints. We establish theoretical properties and computational approaches for this robust version of AG, and illustrate its application to an autonomous vehicle control problem.

New Finite-Time Observers design for a Discrete-Time Switched Linear System

In this work, we consider a discrete-time switched linear system. A novel approach is introduced to estimate its state in a finite fixed time which can be arbitrarily chosen and is independent of the initial state. For cases where the additive disturbance and measurement noise are known, we provide an exact estimation. Otherwise, a finite-time interval observer is designed. The crucial idea is based on using past values of the input and output of the studied system and a minimal dwell time condition. Simulation results are provided to illustrate the effectiveness of the proposed techniques in different scenarios of finite time choices.

An active set solver for constrained $ H_\infty $ optimal control problems with state and input constraints

<p style='text-indent:20px;'>This paper proposes an active set solver for <inline-formula><tex-math id="M2">\begin{document}$ H_\infty $\end{document}</tex-math></inline-formula> min-max optimal control problems involving linear discrete-time systems with linearly constrained states, controls and additive disturbances. The proposed solver combines Riccati recursion with dynamic programming. To deal with possible degeneracy (i.e. violations of the linear independence constraint qualification), constraint transformations are introduced that allow the surplus equality constraints on the state at each stage to be moved to the previous stage together with their Lagrange multipliers. In this way, degeneracy for a feasible active set can be determined by checking whether there exists an equality constraint on the initial state over the prediction horizon. For situations when the active set is degenerate and all active constraints indexed by it are non-redundant, a vertex exploration strategy is developed to seek a non-degenerate active set. If the sampled state resides in a robust control invariant set and certain second-order sufficient conditions are satisfied at each stage, then a bounded <inline-formula><tex-math id="M3">\begin{document}$ l_2 $\end{document}</tex-math></inline-formula> gain from the disturbance to controlled output can be guaranteed for the closed-loop system under some standard assumptions. Theoretical analysis and numerical simulations show that the computational complexity per iteration of the proposed solver depends linearly on the prediction horizon.</p>

Distributionally Robust Model Predictive Control With Total Variation Distance

This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk reformulation of the MPC optimization problem that is distributionally robust in the expected cost and chance constraints. The distributionally robust chance constraint is over-approximated as a simpler, tightened chance constraint that reduces the computational burden. Numerical experiments support our results on probabilistic guarantees and computational efficiency.

A Gradient-Based Event-Driven MPC for Nonlinear Systems With Additive Disturbances Using State-Dependent Thresholds

In this article, we propose a gradient-based event-driven model predictive control (GEMPC) algorithm with a state-dependent threshold for nonlinear systems with additive disturbances and input and state constraints. Firstly, a novel gradient-based event-driven strategy is constructed in the light of the error gradient between the optimal prediction of the state and the real one, which could ensure the Zeno-free property via a positive triggering interval. Subsequently, the novel triggering mechanism and the dual-mode control are combined to establish a GEMPC framework, to further reduce the computing burden and communication transmission especially when the computational resources are limited. Additionally, the feasibility of the GEMPC algorithm and the input-to-state practical stability (ISpS) property of the considered system have been strictly proved in theory. Finally, the simulation comparison results on control of a perturbed nonlinear system are utilized to show the validity of the GEMPC algorithm.

Synchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation

<p style='text-indent:20px;'>The present document outlines a non-linear control theory, based on the PID regulation scheme, to synchronize two second-order dynamical systems insisting on a Riemannian manifold. The devised extended PID scheme, referred to as M-PID, includes an unconventional component, termed 'canceling component', whose purpose is to cancel the natural dynamics of a system and to replace it with a desired dynamics. In addition, this document presents numerical recipes to implement such systems, as well as the devised control scheme, on a computing platform and a large number of numerical simulation results focused on the synchronization of Duffing-like non-linear oscillators on the unit sphere. Detailed numerical evaluations show that the canceling contribution of the M-PID control scheme is not critical to the synchronization of two oscillators, however, it possesses the beneficial effect of speeding up their synchronization. Simulation results obtained in non-ideal conditions, namely in the presence of additive disturbances and delays, reveal that the devised synchronization scheme is robust against high-frequency additive disturbances as well as against observation delays.</p>

Improved offset-free model predictive control utilizing learned model-plant mismatch map

The requirement for a framework that effectively overcomes the limitation of model-based and data-driven control strategies by combining both methods continues to grow. In this study, we propose an approach that learns the model-plant mismatch map and utilizes it based on the offset-free model predictive control (MPC). Specifically, the mismatch map is learned via general regression neural network (GRNN) that has been applied in broad range of fields based on the data from the process, and then the learned mismatch information is provided to the MPC system. In addition, since the approximated mismatch map via GRNN cannot be perfect, an additional supplementary disturbance estimator is utilize to ensure the zero-offset tracking property. Finally, the learned and supplementary disturbance signals are applied to the target problem and the optimal control problem based on the offset-free MPC framework. The effectiveness of the proposed combined model-based and data driven framework is demonstrated by closed-loop simulation. The result shows that the proposed framework can improve the closed-loop tracking performance by utilizing both the learned mismatch information from GRNN and the stabilizing property of the supplementary disturbance estimator.

Triple-A syndrome: A rare cause of addisonian pigmentation

Triple-A syndrome (Allgrove syndrome) is a rare, autosomal recessive disorder classically described with the triad of alacramia, achalasia, and ACTH-resistant adrenal insufficiency. Very few cases have been reported so far in the literature. Rarity leads to misdiagnosis. Phenotypic heterogeneity further adds to the confusion as classical triads are not constantly present in each and every case. The presence of additional autonomic disturbances in some cases brings about the proposal of the name 4A syndrome instead of 3A syndrome. Basic defect is mutation of achalasia, adrenocortical insufficiency, and alacramia syndrome gene. The entity needs multidisciplinary approach including endocrinologist, pediatrician, dermatologist, and ophthalmologist for best possible outcome. Although there is no definitive treatment, early diagnosis is extremely important to save life and prevent neurological sequel from adrenal crisis, to avoid unnecessary investigations and inappropriate treatment, and to improve quality of life. We report a 13-year-old boy with triple-A syndrome diagnosed clinically presented with repeated episodes of seizure, Addisonian pigmentation, the absence of tear, and difficulty of swallowing.

Stochastic Model Predictive Control using Initial State Optimization

We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets to design the MPC. The scheme avoids the infeasibility issues arising from unbounded disturbances by including the initial state as a decision variable. We show that the stabilizing control scheme can guarantee constraint satisfaction in closed loop, assuming unimodal disturbances. In addition to illustrating these guarantees, the numerical example indicates further advantages of optimizing over the initial state for the transient behavior.

A Current Harmonic Suppression Method for PMSM Based on Harmonic Prediction Adaptive Notch Filter

The adaptive filters (ANF) have been commonly used in current harmonic suppression. However, the digital delay will narrow the stability region and its harmonic suppression performance will be deteriorated at high-speed region. To overcome this problem, this paper proposed two modified ANF. Combining with the deadbeat current (DBC) controller, the effect of digital delay on ANF is analyzed. A simple one step harmonic prediction method (OSPANF) is proposed to replace the traditional steepest gradient method (SGM). Based on the OSPANF, the current can be controlled stably in the high-speed area and the harmonic suppression effect is better than the traditional notch filter. Through bode diagram analysis, OSPANF will have a harmonic amplification peak near the set notch frequency, which may bring additional disturbances. Thus, a two steps prediction adaptive notch filter (TSPANF) is implemented. Through the Experimental results, it can be proved that the proposed TSPANF method has better harmonic suppression effect in the high-speed area than OSPANF and the stability region of the proposed two methods is larger than the traditional method.

Robust Nonlinear Model Predictive Control With Model Predictive Sliding Mode for Continuous-Time Systems

Abstract This paper presents a robust, tube-based nonlinear model predictive controller for continuous-time systems with additive disturbances which cascades two sampled-data model predictive controllers: the first creates a desired path using nominal dynamics, and the second maintains the true state close to the nominal state by regulating a sliding variable designed on the error between the true and nominal states. The sampled-data model predictive approach permits easy incorporation of continuous-time sliding mode dynamics, allowing a dynamic boundary layer and tube design to be included. In this way, the control applied to the system capitalizes on the robustness properties of traditional sliding mode control (SMC) while incorporating system constraints. Stability analysis is presented in the context of input-to-state stability (ISS) for continuous-time systems. The proposed controller is implemented on two case studies, is compared to benchmark tube-based model predictive controllers, and is evaluated using average root-mean-square (RMS) values on the state and input variables, in addition to average integral square error (ISE) and integral absolute error (IAE) values on the position states. Results reveal that the proposed technique responds to higher levels of disturbance with significant increases in control effort, eliminates constraint violation by using of constrained SMC as the secondary controller, and maintains similar tracking performance to benchmark controllers at lower levels of control effort.

Ecosystem Response Through a Resilience Lens: Do Differences in the Illinois River Over 150 Y Indicate Regime Shifts?

AbstractMost of the world's large river ecosystems are subject to multiple anthropogenic stressors including climate change, disconnection between the main river channel and floodplain, flow regulation, and land‐use modification. Viewed through a resilience lens, these ecosystems are potentially in a new regime, exhibiting a different structure, function, and set of feedbacks. We investigated the trophic status and food web character response to anthropogenic stressors over 150 years in the Illinois River. Differences in stable isotope ratios, community niche space, basal resource contribution to higher levels in the food web, mean trophic position of fish functional feeding guilds, and food chain length among four stressor phases suggest changes in ecosystem function in the Illinois River. Moreover, the river did not return to pre‐stressor conditions following watershed‐wide restoration efforts. Differences in trophic status and food web character also varied between the upper‐ and lower‐river zones of the Illinois River over time. This spatial divergence further highlights the complexity of responses to multiple stressors in this ecosystem. Overall, differences in trophic status and food web character suggest a shift to a new regime–an Anthropocene regime–and one that has a reduced capacity to absorb additional disturbances. Given human pressures are a global issue, our results based on a 150 years data set, could assist in the management of riverine landscapes that face regime shifts due to human stressors.

Resource allocation procedures for unknown sales response functions with additive disturbances

We develop a modified exploration–exploitation algorithm which allocates a fixed resource (e.g., a fixed budget) to several units with the objective to attain maximum sales. This algorithm does not require knowledge of the form and the parameters of sales response functions and is able to cope with additive random disturbances. Note that additive random disturbances, as a rule, are a component of sales response functions estimated by econometric methods. We compare the developed algorithm to three rules of thumb which in practice are often used to solve this allocation problem. The comparison is based on a Monte Carlo simulation for 384 experimental constellations, which are obtained from four function types, four procedures (including our algorithm), similar/varied elasticities, similar/varied saturations, high/low budgets, and three disturbance levels. A statistical analysis of the simulation results shows that across a multi-period planning horizon the algorithm performs better than the rules of thumb considered with respect to two sales-related criteria.

A multi-agent and internet of things framework of digital twin for optimized manufacturing control

ABSTRACT The demand for customized products is increasing, which brings great challenges to the traditional manufacturing system. The traditional manufacturing system lacks the analysis and feedback of the data collected in manufacturing, which hinders the rational utilization of the resources. In order to reasonably allocate resources according to the production requirements and effectively avoid the influence of external interference on the manufacturing system, a framework for the intelligent digital twin shopfloor is proposed in this paper. The framework consists of three primary components, namely physical shopfloor, virtual shopfloor, and digital twin service system. A model of digital twin shopfloor, a self-organizing model which achieves automation function in physical shopfloor, and an adaptive model which provides additional external disturbance resistance in virtual shopfloor are developed to improve the above-mentioned components. The mechanism of a contract network protocol and some cooperation strategies used in multi-agents are applied to achieve the capabilities above, which improve the reconfiguration and response ability of the shopfloor. A design case is studied to illustrate that the intelligent digital twin shopfloor can configure resources and deal with disturbances effectively.

Robust Platoon Control in Mixed Traffic Flow Based on Tube Model Predictive Control

The design of cooperative adaptive cruise control is critical in mixed traffic flow, where connected and automated vehicles (CAVs) and human-driven vehicles (HDVs) coexist. Compared with pure CAVs, the major challenge is how to handle the prediction uncertainty of HDVs, which can cause significant state deviation of CAVs from planned trajectories. In most existing studies, model predictive control (MPC) is utilized to replan CAVs' trajectories to mitigate the deviation at each time step. However, as the replan process is usually conducted by solving an optimization problem with information through inter-vehicular communication, MPC methods suffer from heavy computational and communicational burdens. To address this limitation, a robust platoon control framework is proposed based on tube MPC in this paper. The prediction uncertainty is dynamically mitigated by the feedback control and restricted inside a set with a high probability. When the uncertainty exceeds the set or additional external disturbance emerges, the feedforward control is triggered to plan a ``tube'' (a sequence of the set), which can bound CAVs' actual trajectories. As the replan process is usually not required, the proposed method is much more efficient regarding computation and communication, compared with the MPC method. Comprehensive simulations are provided to validate the effectiveness of the proposed framework.

Stochastic Distributed Predictive Tracking Control Under Inexact Minimization

In this article, we propose a chance-constrained cooperative distributed model predictive control scheme for reference tracking. We consider dynamically coupled linear time-invariant systems that are subject to local and coupling chance constraints. The proposed controller is based on the distributed alternating direction method of multipliers and is able to steer the system to any admissible setpoint while ensuring recursive feasibility under inexact dual optimization and unbounded additive disturbances. Under a central convex unimodality assumption, the chance constraints are guaranteed to hold in closed loop. This article closes with two numerical examples. The first one is of an academic nature in order to highlight the chance constraint satisfaction, convergence, and numerical properties of the proposed algorithm. The second one is a practical scenario of a benchmark process.

On homogeneous controllability functions

The controllability function method, introduced by V. I. Korobov in late 1970s, is known to be an efficient tool for control systems design. It is developed for both linear/nonlinear and finite/infinite dimensional systems. This paper bridges the method with the homogeneity theory popular today. The standard homogeneity known since 18th century is a symmetry of function with respect to uniform scaling of its argument. Some generalizations of the standard homogeneity were introduced in 20th century. This paper shows that the so-called homogeneous norm is a controllability function of the linear autonomous control system and the corresponding closed-loop system is homogeneous in the generalized sense. This immediately yields many useful properties known for homogeneous systems such as robustness (Input-to-State Stability) with respect to a rather large class of perturbations, in particular, with respect to bounded additive measurement noises and bounded additive exogenous disturbances. The main theorem presented in this paper slightly refines the design of the controllability function for a multiply-input linear autonomous control systems. The design procedure consists in solving subsequently a linear algebraic equation and a system of linear matrix inequalities. The homogeneity itself and the use of the canonical homogeneous norm essentially simplify the design of a controllability function and the analysis of the closed-loop system. Theoretical results are supported with examples. The further study of homogeneity-based design of controllability functions seems to be a promising direction for future research.

Parametric Design of Functional Interval Observer for Time-Delay Systems with Additive Disturbances

Parametric Design of Functional Interval Observer for Time-Delay Systems with Additive Disturbances

Event-Based MPC for Nonlinear Systems with Additive Disturbances: A Quasi-Differential Type Approach

By integrating the event-based mechanism and the model predictive control (MPC) method, an improved event-based MPC framework is constructed for the nonlinear control problem subject to disturbances. Firstly, a new event-triggering condition is suggested, which is constructed on the basis of the gradients of the differences between the optimal state prediction and the actual one at two consecutive sample times. Then, an event-based MPC algorithm is further proposed, in which the dual-mode control technique is incorporated to handle the nonlinear perturbed system. Furthermore, it is strictly demonstrated that the proposed algorithm will ensure the feasibility of the MPC method and the stability of the considered system, while significantly decreasing the number of solving optimization problems, based on which resources for information transfer can be effectively saved. Finally, simulations and comparisons are shown to verify the efficacy of the proposed framework.

Stochastic Time-Varying Model Predictive Control for Trajectory Tracking of a Wheeled Mobile Robot

In this paper, a stochastic model predictive control (MPC) is proposed for the wheeled mobile robot to track a reference trajectory within a finite task horizon. The wheeled mobile robot is supposed to subject to additive stochastic disturbance with known probability distribution. It is also supposed that the mobile robot is subject to soft probability constraints on states and control inputs. The nonlinear mobile robot model is linearized and discretized into a discrete linear time-varying model, such that the linear time-varying MPC can be applied to forecast and control its future behavior. In the proposed stochastic MPC, the cost function is designed to penalize its tracking error and energy consumption. Based on quantile techniques, a learning-based approach is applied to transform the probability constraints to deterministic constraints, and to calculate the terminal constraint to guarantee recursive feasibility. It is proved that, with the proposed stochastic MPC, the tracking error of the closed-loop system is asymptotically average bounded. A simulation example is provided to support the theoretical result.