Nonsmooth Control Research Articles

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.

Constructing Reachable Sets for a Class of Nonsmooth Control Systems on a Plane

Constructing Reachable Sets for a Class of Nonsmooth Control Systems on a Plane

Distributed Coverage Hole Prevention for Visual Environmental Monitoring With Quadcopters Via Nonsmooth Control Barrier Functions

Distributed Coverage Hole Prevention for Visual Environmental Monitoring With Quadcopters Via Nonsmooth Control Barrier Functions

Cooperative optimal train operation algorithm for utilizing regenerative braking energy

The efficient use of regenerative braking energy between trains can significantly reduce the net traction energy consumption in urban rail transit systems, and has attracted considerable attention in recent years. An effective way of using regenerative braking energy is to adjust the train's coasting or cruising phase to an acceleration phase to match the braking phase of a nearby train within the same substation. This paper formulates the train driving phase adjustment problem as a cooperative optimal control problem, where a novel energy constraint is introduced to ensure efficient use of regenerative braking energy during the adjusted phase with optimal traction effort. By applying the control parameterisation method and elaborate handling of the energy constraint and the non-smooth control bound constraint, we transform the formulated problem into a nonlinear programming problem. We then use the sequential quadratic programming algorithm to solve the resulting problem, with the gradients of the cost and constraint functions computed using the sensitivity method. Numerical examples based on real-world data for a subway line show the effectiveness of the proposed method and its advantages over a genetic algorithm in terms of energy savings and computational efficiency.

Distributed Multiagent-Based Event-Driven Fault-Tolerant Control of Islanded Microgrids.

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Model predictive control based on air pressure forecasting of OWC wave power plants

Ocean waves hold a promising potential as a sustainable source of clean energy. However, in order to make wave energy converters financially viable, particularly in the case of the oscillating water column (OWC), it is crucial to optimize the power take-off system to maximize performance. Most control strategies focus solely on turbine performance, often at the expense of overlooking the overall wave-to-wire system performance. Therefore, a model predictive control (MPC) strategy using short-term air pressure prediction was proposed to enhance electrical energy delivered to the grid. The Mutriku wave power plant (Spain) was case-studied for evaluating the control approaches, which focused on maximizing average power (turbine or generator) from an OWC equipped with the innovative biradial turbine. In comparison to the reference baseline strategy, the implementation of MPC (with a 16-second forecast) resulted in a minor 2%-increase in the average turbine power. However, when it comes to the generator power accumulated over a year, the MPC strategy produced an improvement of more than 8%. Since generator power is the ultimate product, this improvement is significant. Nonetheless, the MPC strategy exhibited a non-smooth control response compared to other strategies. Improving control action quality should be a primary focus of future research.

Nonsmooth Control Barrier Function design of continuous constraints for network connectivity maintenance

This paper considers the problem of maintaining global connectivity of a multi-robot system while executing a desired coordination task. Our approach builds on optimization-based feedback design formulations, where the nominal cost function and constraints encode desirable control objectives for the resulting input. Our solution uses the algebraic connectivity of the multi-robot interconnection topology as a control barrier function and critically embraces its nonsmooth nature. We take advantage of the understanding of how Laplacian eigenvalues behave as their multiplicities change, in combination with the flexibility provided by the concept of control barrier function, to carefully design additional constraints that guarantee the resulting optimization-based controller is continuous and maintains network connectivity. The technical treatment combines elements from set-valued theory, nonsmooth analysis, and algebraic graph theory to imbue the proposed constraints with regularity properties so that they can be smoothly combined with other control constraints. We provide simulations and experimental results illustrating the effectiveness and continuity of the proposed approach in a resource gathering problem.

Decentralized Adaptive Fuzzy Finite-Time Event-Triggered Control for Interconnected Nonlinear Systems Subject to Input Saturation

This article investigates the decentralized adaptive finite-time command filter control for interconnected nonlinear systems subject to input saturation by event-triggered (ET) output feedback. In practice, some subsystems may be distributed distantly, making it difficult for a centralized controller to acquire feedback signals from them. On the other hand, the finite-time control scheme with a nonsmooth controller could be used for accelerating the system convergence rate. However, with this control scheme, it is difficult to exclude Zeno behavior directly by using the existing methods. To overcome these obstacles, we consider a decentralized control scheme and exploit the property of hyperbolic tangent functions and the approximation capability of fuzzy logic systems to handle interconnected nonlinear functions. Furthermore, we develop a new switching-type finite-time ET mechanism in the presence of asymmetric input saturation. Under the developed decentralized controller, all system states are bounded as well as the tracking error converges to a compact set near the origin in a finite time. Meantime, the function's one-sided differentiability is employed to avoid Zeno phenomenon. Finally, two practical examples are provided to demonstrate the effectiveness and advantages of the presented approach.

Dynamical analysis of a [formula omitted] epidemic-like propagation model with non-smooth control

The continuous acceleration of information communication makes the spread of rumors constantly develop and change. Analysis of the dynamics of rumor propagation allows for its better control. In this paper, we study a rumor transmission model with a nonlinear transmission rate and a non-smooth threshold transmission function, based on the classical SI infectious disease model. In this model, we first prove the existence of the model solutions, and then obtain the number of non-negative equilibrium points. By dividing the model into spatially homogeneous and inhomogeneous parts with continuous and discontinuous, we discuss the characteristic equations of the equilibrium points and obtain the existence conditions for Saddle–node bifurcation, Turing bifurcation and Hopf bifurcation under the corresponding conditions. Finally, the feasibility of the theoretical calculation results is further verified by using the simulation results.

Stability and Robustness Analysis of Finite-Time Consensus Algorithm for Second-Order Multiagent Systems Under Sampled-Data Control

The consensus problem for second-order multiagent systems based on nonsmooth sampled-data control is considered. First, a continuous-time nonsmooth consensus protocol is proposed, which can realize the consensus of systems in a finite time when the external disturbance is absent. Next, based on the sampled data and the zero-order holder, a new discrete-time nonsmooth protocol is proposed. Considering external disturbances, the explicit relationship between the ultimate boundary of errors of any two agents and the sampling period and external disturbance is given with the Lyapunov method and graph theory, which theoretically shows that the nonsmooth control algorithm has a stronger ability to resist external disturbance than the smooth control algorithm. Finally, a simulation example shows the superiority of the nonsmooth consensus algorithm over a smooth consensus algorithm.

Optimal Safety for Constrained Differential Inclusions Using Nonsmooth Control Barrier Functions

For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs. Through the use of nonsmooth analysis tools, we show that a continuous optimal control law can be selected from a set-valued constraint capturing the system constraints and conditions guaranteeing safety using control barrier functions. Our results guarantee optimality and safety via a continuous state-feedback law designed using nonsmooth control barrier functions. An example pertaining to obstacle avoidance with a target illustrates our results and the associated benefits of using nonsmooth control barrier functions.

Bifurcation and chaos for a novel model of trigonal centrifugal governor with non-smooth control

Bifurcation and chaos for a novel model of trigonal centrifugal governor with non-smooth control

Nonsmooth Observer-Based Sensorless Speed Control for Permanent Magnet Synchronous Motor

The sensorless speed regulation problem for a surface-mount permanent magnet synchronous motor system is studied in this article. First, a new nonsmooth observer scheme is proposed to estimate the rotor position, speed, and lumped disturbance of the system. Based on the estimated information, a composite speed controller is then designed, in which the nonsmooth control technique is employed in the feedback design, and the estimated value of disturbance is used in the feedforward compensation. By Lyapunov theory, rigorous analysis guarantees the stability of the closed-loop system and shows that the proposed method can enhance the disturbance rejection property of the system. Finally, simulation tests and experiment results are given to verify the effectiveness of the proposed method.

Dynamic event‐triggered control for a class of p‐normal nonlinear time‐delay systems via output feedback

ABSTRACTIn this article, the event‐triggered (ET) output feedback control problem is discussed for a class of ‐normal nonlinear time‐delay systems. Different from the related existing literature, the linear growth condition is relaxed to the homogeneous one and the growth rate is unknown. In the case of unknown time‐varying delays and control coefficients, nonsmooth control law and some extra redundant terms will be encountered in the design of ET controller, which would bring substantial challenges to the achievement of global convergence. To cope with unknown growth rate and time‐varying delays, two dynamic gains and an appropriate Lyapunov–Krasovskii functional (LKF) are introduced. Then, a new dynamic ET mechanism is given, in which the triggering threshold can be tuned dynamically. It is proved that all the signals of the closed‐loop system (CLS) are bounded. Corresponding examples are given to indicate the validity of the developed theoretical results.

Dynamics of a reaction-diffusion rumor propagation model with non-smooth control

To reflect the government and media refutation to rumor propagation, we have established a reaction-diffusion rumor propagation model by considering a non-smooth control function. Firstly, we obtain the rumor propagation threshold according to the next generation matrix theory, prove the existence and uniqueness of solution and discuss the existence of the equilibrium points. Secondly, we discuss the stability of the equilibrium points with the impact of the spatial diffusion. Thirdly, the conditions for spatially homogeneous and discontinuous Hopf bifurcation are presented. Finally, several numerical simulations are given to show the possible impact, and the factors affecting rumor propagation are theoretically analyzed, which proves the validity of the theoretical analysis.

A finite time composite control method for quadrotor UAV with wind disturbance rejection

The quadrotor UAV is subject to wind disturbance during flight, which causes attitude deviation and oscillation. To improve anti-wind disturbance performance, this work offers a reduced-order generalized proportional–integral observer-based wind-disturbance control strategy for quad-rotor UAVs (RGPIO). To improve the disturbance rejection property of quadrotor UAV systems, this work offers a composite control approach based on reduced-order generalized proportional–integral observer (RGPIO) and nonsmooth control. To begin, an RGPIO is used to evaluate system disruptions. In the feed-forward compensation scheme, the anticipated value is used. Second, the feedback design employs a nonsmooth feedback control method. The controller’s stability is then checked. When compared to the standard PID control technique, the experimental findings show that the suggested control method successfully suppresses the wind disturbance.

An Extended Kalman Filter for Nonsmooth Attitude Control Design of Quadrotors using Quaternion Representation

This paper proposed Extended Kalman Filter specifically designed for nonlinear and nonsmooth control system applied in Autonomous Quadrotor Control such as sliding mode control. Many controllers focused on global stability usually consider exact parameters through measurements. Such assumptions are not always possible due to the unavailability of sensors or unmeasurable state in real-life condition. In this paper, we consider only the angular velocity is possible for measurement, i.e., only gyroscope measurement is available. This condition is known as omega-state-measurement (OSM). Without loss of generality, for theoretical simplification beside gyroscope measurement, we assume the orientation measurement represented in quaternion is also available. Additive random gaussian noise is included to the measurement model to be used in Kalman Filter. Finally the proposed Extended Kalman Filter implemented in a PD Sliding Mode controller is simulated using many scenarios to verify its effectiveness. The Kalman Filter works well in spite of model error and disturbance.

Distributed finite‐time formation control of multiple Euler–Lagrange systems under directed graphs

This paper investigates the finite-time formation problem of multiple Euler–Lagrange systems subject to model uncertainties and external disturbances under directed graphs. An adaptive distributed control approach is developed by integrating dynamic gain control and adaptive control based on the consensus theory and the finite-time stability theory. Auxiliary scalar dynamics are constructed to facilitate dynamic gain design. It is shown that finite-time formation can be achieved via the proposed non-smooth controller characterized by fractional powers of the auxiliary dynamics, which is significantly different from most existing works on finite-time controllers where fractional powers of system states are adopted. Moreover, continuity of the proposed controller is guaranteed by adjusting one control parameter, of which range is proven explicitly. In addition, dynamic surface control is improved to remove acceleration information from finite-time controller design. In the end, the effectiveness of the proposed control approach is verified by numerical simulation.

Non-Smooth Control Barrier Navigation Functions for STL Motion Planning.

This paper reports on a new approach to Signal Temporal Logic (STL) control synthesis, that 1) utilizes a navigation function as the basis to construct a Control Barrier Function (CBF), and 2) composes navigation function-based barrier functions using nonsmooth mappings to encode Boolean operations between the predicates that those barrier functions encode. Because of these two key features, the reported approach 1) covers a larger fragment of STL compared to existing approaches, 2) alleviates the computational cost associated with evaluation of the control law for the system in existing STL control barrier function methodologies, and 3) simultaneously relaxes some of the conservativeness of smooth combinations of barrier functions as a means of implementing Boolean operators. The paper demonstrates the efficacy of this new approach with three simulation case studies, one aiming at illustrating how complex STL motion planning specification can be realized, the second highlights the less-conservativeness of the approach in comparison to the existing methods, and another that shows how this technology can be brought to bear to push the envelope in the context of human-robot social interaction.

A new data-driven sliding mode learning control for discrete-time MIMO linear systems

A new data-driven sliding mode learning control (DDSMLC) is designed for a class of discrete-time MIMO linear systems in the presence of uncertainties. In this scheme, a new control is designed to enforce the states to reach and remain on the sliding surface. In addition, a recursive algorithm using system measured data is adopted to estimate the unknown system parameters, so a complete data-driven sliding mode control is designed, which does not need to know any parameters in the system. Moreover, the chattering is reduced because there is no non-smooth control used in DDSMLC. After the strict stability analysis, the effectiveness of DDSMLC is validated by MATLAB simulations.