Parameter-dependent Controller Research Articles

Stabilization of polytopic discrete-time varying systems with rate and magnitude saturating actuators and bounded disturbances

This study tackles the critical challenge of designing parameter-dependent controllers for the wide class of discrete-time polytopic systems under rate and magnitude saturating actuators. Such a class finds widespread use in diverse applications spanning from medicine to industrial engineering. Our central contribution lies in developing novel convex parameter-dependent state feedback controller synthesis conditions that ensure regional and input-to-state stability, effectively mitigating the adverse effects of rate and magnitude-saturating actuators. Our approach considers the ℓ2/ℓ∞ gain between disturbance input and controlled output, offering performance specifications and retaining validity for specific initial conditions and amplitude-limited input disturbances. Moreover, our methodology is highly adaptable and suitable for a broad spectrum of systems, including LPV/quasi-LPV and T-S fuzzy systems. We leverage the position-type feedback model with speed limitation (PMSL) and the generalized sector condition to derive our controller synthesis method, resulting in a parallel-distributed-compensation strategy under standard assumptions, ensuring practicality and applicability to diverse system requirements. To highlight the effectiveness of our approach, we present numerical examples for comparative evaluation concerning the existing literature. Furthermore, we validate our methodology through real-time experiments conducted on a nonlinear coupled tank system, providing concrete evidence of its efficacy and feasibility for real-world implementation.

State observer-based Physics-Informed Machine Learning for leader-following tracking control of mobile robot

In this paper, the novel leader-following tracking control method is proposed for mobile robots, which consists estimation technique of the speed of the leader robot (LR), and a parameter-dependent controller for the follower robot (FR). To estimate the speed of LR, a novel Physics Informed Machine Learning (PIML) is proposed to learn the dynamics of the state observer via the error state model. The dynamics of the state observer in PIML play a significant role for stable learning and state estimation of uncertain models. The gain of the parameter-dependent controller is determined by the convex combination of the robust control technique via the polytopic model. Finally, the tracking performance of the proposed method is verified through the simulation and experiment.

Process-Structure-Property Interdependencies in Non-Isothermal Powder Bed Fusion of Polyamide 12

Non-isothermal laser-based powder bed fusion (LPBF) of polymers suggests the potential for significantly extending the range of materials applicable for powder-based additive manufacturing of polymers, relying on the absence of a material-specific processing window. To allow for the support-free manufacturing of polymers at a build chamber temperature of 25 °C, applied processing strategies comprise the combination of fractal exposure strategies and locally quasi-simultaneous exposure of distinct segments of a particular cross section for minimizing crystallization-induced part deflection. Based on the parameter-dependent control of emerging cooling rates, formed part morphologies and resulting mechanical properties can be modified. Thermographic in situ measurements allow for correlating thermal processing conditions and crystallization kinetics with component-specific mechanical, morphological, and microstructural properties, assessed ex situ. Part morphologies formed at crystallization temperatures below 70 °C, induced by reduced laser exposure times, are characterized by a nano-spherulitic structure, exhibiting an enhanced elongation at break. An ambient temperature of 25 °C is associated with the predominant formation of a combined (α + γ)-phase, induced by the rapid cooling and subsequent laser-induced tempering of distinct layers, yielding a periodic microstructural evolution. The presented results demonstrate a novel approach for obtaining nano-spherulitic morphologies, enabling the exposure-based targeted adaption of morphological properties. Furthermore, the thermographic inline assessment of crystallization kinetics allows for the enhanced understanding of process-morphology interdependencies in laser-based manufacturing processes of semi-crystalline polymers.

Memoryless parameter-dependent control strategy of stochastic strict-feedback time delay systems

For a class of stochastic strict-feedback nonlinear systems subject to different time delay states, this paper mainly concerns the problem of global asymptotic stabilization. Two new control strategies that the memoryless parameter-dependent state feedback control and the memoryless parameter-dependent output feedback control are taken into consideration, respectively. By skillfully constructing the Lyapunov-Krasovskii (L-K) functional, taking the proper determined parameter and employing the stochastic nonlinear time delay system (SNTDS) stability theory, the global asymptotic stability of the stochastic closed-loop system can be achieved. The proposed output feedback control scheme is finally utilized for the control design of the one-link manipulator system and two-stage chemical reactor system, which can verify the availability of the control approach.

Static output feedback H∞ control for switched LPV time-delay systems with nonlinear constraints

This paper addresses the issues of static output feedback [Formula: see text] control for switched linear parameter-varying (LPV) time-delay systems using multiple parameter-dependent Lyapunov functions. First, a parameter and state-dependent switching strategy with dwell time is designed and a sufficient condition ensuring the stability of the unforced switched LPV time-delay systems is established with the aid of the switching law. Then, the piecewise parameter-dependent controller is designed, such that the closed-loop system is asymptotically stable and satisfies an [Formula: see text] performance index. Finally, two examples are provided to show the effectiveness of the results.

Synchronization of multiple reaction–diffusion memristive neural networks with known or unknown parameters and switching topologies

This paper investigates the synchronization problems of multiple reaction–diffusion memristive neural networks (MRDMNNs) with known or unknown parameters and switching topologies via distributed control. In complex environment, the proposed system may face switching topologies, diffusion effects, external disturbance, parameter mismatch or uncertainty, so designing security control laws to synchronize the proposed system is a enormous challenge. The parameter mismatch terms herein are extended to be unbounded, which is different from the general boundedness hypothesis. Since the parameter mismatch term would be known or unknown, we design a novel parameter-dependent controller for the known condition and a novel parameter-independent adaptive controller for the unknown condition respectively. By constructing new Lyapunov functions, using some properties of M-matrix and robust control method, the synchronization errors will all converge into a bound set via the two designed nonlinear controllers. And we are able to select appropriate control parameters to control the upper bound. Moreover, the obtained theorems can determine the feedback control gains, which can be used for security control. Finally, two numerical simulations are given to support the obtained theoretical results.

Parameter-dependent controller design of stochastic strict feedforward nonlinear systems

In this paper, the exponentially stable problem is discussed for a class of stochastic strict feedforward nonlinear systems. Firstly, by employing the proper coordinate transformation and the novel parameter-dependent controller, the initial stochastic strict feedforward nonlinear system is converted to an equivalent system. After that, the implementable parameter-dependent controller, which is adopted to handle the nonlinearities, can be achieved by reasonably selecting the designed parameter. Finally, by means of stochastic Lyapunov stability theory, it is rigorously verified that the proposed parameter-dependent state-feedback controller and parameter-dependent output-feedback controller can guarantee that the stochastic closed-loop system is the fourth moment exponentially stable. Simulation results demonstrate the efficiency of the proposed parameter-dependent controller.

Polynomially parameter dependent exponential stabilization of sampled-data LPV systems

This paper proposes a polynomially sampled parameter dependent controller design for sampled-data linear parameter varying (LPV) systems. The goal of this study is to design a controller which exponentially stabilizes the system with a larger maximum sampling interval. To achieve this, we utilize the information of the parameters in the controller part. The proposed controller is dependent on the polynomials with respect to the sampled parameters, which is more effective to stabilize the system with a larger maximum sampling interval. To design the controller, an exponential stabilization condition is derived from a new Polynomially Parameter Dependent Quadratic Lyapunov Function with Looped-Functionals (PPDQLLF) which is dependent on the parameters of a plant. The derived condition is represented in terms of the linear matrix inequality (LMI) and it is formulated as sum of squares (SOS) conditions to obtain feasible solutions. The effectiveness of the proposed method is shown by the simulation results of numerical examples.

Multi-objective Unified qLPV Observer: Application to a Semi-active Suspension System

Abstract This work concerns the design of a multi-objective unified qLPV observer for the state estimation problem in LPV systems with a parameter-dependent control input matrix. The standard forms of the system and the observer are first presented, where the observer matrices are functions of the estimated states (qLPV problem). The effects of bounded unknown input disturbances are decoupled from the estimation error thanks to the parameterization of the observer matrices. To treat the disturbance caused by inexact scheduling parameters, we introduce an upper bound on the parameter estimation error, which is considered uncertainty. Then, the effects of the control input and the random measurement noise on the estimation error are minimized using the H∞ and generalized H2 conditions, respectively, as a multi-objective optimization problem. In the solution of the LMI sets, the projection lemma is applied to reduce the high conservativeness that would otherwise lead to suboptimal results. Then this observer is applied to a semi-active automotive suspension system written in LPV form, using simulations with real data measured from our experiment test platform, and compared with the linear time-invariant H∞ and H2 observers.

Adaptive tracking synchronization for coupled reaction–diffusion neural networks with parameter mismatches

In this paper, tracking synchronization for coupled reaction–diffusion neural networks with parameter mismatches is investigated. For such a networked control system, only local neighbor information is used to compensate the mismatch characteristic termed as parameter mismatch, uncertainty or external disturbance. Different from the general boundedness hypothesis, the parameter mismatches are permitted to be unbounded. For the known parameter mismatches, parameter-dependent controller and parameter-independent adaptive controller are respectively designed. While for fully unknown network parameters and parameter mismatches, a distributed adaptive controller is proposed. By means of partial differential equation theories and differential inequality techniques, the tracking synchronization errors driven by these nonlinear controllers are proved to be uniformly ultimately bounded and exponentially convergent to some adjustable bounded domains. Finally, three numerical examples are given to test the effectiveness of the proposed controllers.

Reduced Basis Methods---An Application to Variational Discretization of Parametrized Elliptic Optimal Control Problems

We consider a class of parameter dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, to...

Parameter-dependent transmission dynamics and optimal control of foot and mouth disease in a contaminated environment

The problem of foot and mouth disease (FMD) is of serious concern to the livestock sector in most nations, especially in developing countries. This paper presents the formulation and analysis of a deterministic model for the transmission dynamics of FMD through a contaminated environment. It is shown that the key parameters that drive the transmission of FMD in a contaminated environment are the shedding, transmission, and decay rates of the virus. Using numerical results, it is depicted that the host-to-host route is more severe than the environmental-to-host route. The model is then transformed into an optimal control problem. Using the Pontryagin’s Maximum Principle, the optimality system is determined. Utilizing a gradient type algorithm with projection, the optimality system is solved for three control strategies: optimal use of vaccination, environmental decontamination, and a combination of vaccination and environmental decontamination. Results show that a combination of vaccination and environmental decontamination is the most optimal strategy. These results indicate that if vaccination and environmental decontamination are used optimally during an outbreak, then FMD transmission can be controlled. Future studies focusing on the control measures for the transmission of FMD in a contaminated environment should aim at reducing the transmission and the shedding rates, while increasing the decay rate.

Control of a small helicopter with linear matrix inequality-based design assuring stability and performance

This article focuses on linear matrix inequality-based controller designs that can achieve stabilization and reference tracking for a small unmanned helicopter at various flight conditions. A nonlinear mathematical model of a small-scale helicopter is constructed. Then trim conditions are found and linearized around different equilibrium points. Local [Formula: see text] controllers are designed at trim conditions based on the local linear models. The pointwise controllers achieve local stability and performance, but fail at stabilization and tracking over the full envelope. A scheduling controller is built by blending the local controller outputs. In addition, grid-based [Formula: see text] controllers are designed at each operating point with common Lyapunov function. This allows controller scheduling between the adjacent design points with guaranteed stability and performance across the design envelope. Based on the family of linear systems which are obtained from the nonlinear model, an affine parameter-dependent model is built to exploit the approximate linear parameter dependency. Then, a parameter-dependent linear parameter varying controller is synthesized for the affine parameter-dependent model. Although local performance is satisfactory for all given design methods, local [Formula: see text] controllers and affine parameter-dependent controller cannot yield satisfactory performance over the full flight envelope apart from the grid-based controller with common Lyapunov function approach.

Finite-time control in probability for time-varying systems with measurement censoring

This paper considers a parameter-dependent controller design problem for a class of discrete-time uncertain systems subject to censored measurement. First, a set of mutually independent stochastic variables obeying uniform distribution is used to describe the system uncertainty. Then, an array of new bounded variables is introduced to characterize the boundedness of the censored measurement. In addition, a novel definition, named as finite-time boundedness in probability (FTBP), is presented to depict the dynamic behavior of addressed systems in the sense of probability. In this case, the norm of controlled system states cannot exceed a given boundary under a probability constraint. By means of the hyper-rectangle depending on the value range of stochastic variables, a sufficient condition is presented to ensure that the system is FTBP. Finally, the corresponding controller design problem is formulated as an algorithm based on the recursive linear matrix inequality. Two simulation examples are given to illustrate the effectiveness of the proposed methodology.

H∞ fault-tolerant control for switched linear parameter-varying systems: A parameter and state-dependent switching method with dwell time

This article discusses the issue of H∞ fault-tolerant control for switched linear parameter-varying systems with actuator failures using the multiple discretized parameter-dependent Lyapunov functions method. A key point of this work is to construct the multiple discretized parameter-dependent Lyapunov functions, which provide an effective tool for avoiding the Zeno behavior generated by the parameter and state-dependent switching approach. This is not a simple extension of traditional multiple Lyapunov functions because of the introduction of external parameter and dwell time. First, a switching strategy depending on the parameter, state and dwell time is proposed, which gets rid of the assumption of finite number of switchings on any finite time. Then, the parameter-dependent controller is designed which, together with the parameter and state-dependent switching law with dwell time, can guarantee the [Formula: see text] performance of the closed-loop switched linear parameter-varying system for all admissible actuator failures. Finally, a turbofan engine example is given to demonstrate the applicability of the main results.

Feedback passification for switched LPV systems via a state and parameter-triggered switching with dwell time constraints

This paper addresses the issues of passivity and passification for switched linear parameter-varying (LPV) systems using multiple parameter-dependent storage functions which are not a simple extension of traditional multiple storage functions because of the introduction of the external parameter. Firstly, a state and parameter-triggered switching strategy is designed. The switching law is different from the existing results, which guarantees a dwell time constraint even when all subsystems are not passive. Then, an analysis condition ensuring the passivity for switched LPV systems is presented with the aid of the switching law. When passivity cannot be guaranteed by the designed switching law, the dual design scheme of parameter-dependent controllers for subsystems and a switching law is constructed to solve the problem of feedback passification for the switched LPV system. Finally, an aero-engine control example is provided to demonstrate the feasibility of the theoretical results.

Trajectory tracking of AGVs by linear parameter-varying control: a case study

This paper proposes a linear-parameter varying (LPV) controller design approach for trajectory tracking of an automated guided vehicle (AGV) based on a simple yet nonlinear kinematic model. By linearization of the model about a reference trajectory, an LPV model is readily obtained, which is then augmented with identified linear time-invariant actuator models. An appropriate parameter-dependent controller for the system is designed in an optimal way by specifying the control objectives in terms of H∞ criteria. Its performance is assessed by means of experiments on the considered prototype of an autonomous platform.

A Multiscale Understanding of the Thermodynamic and Kinetic Mechanisms of Laser Additive Manufacturing

Abstract Selective laser melting (SLM) additive manufacturing (AM) technology has become an important option for the precise manufacturing of complex-shaped metallic parts with high performance. The SLM AM process involves complicated physicochemical phenomena, thermodynamic behavior, and phase transformation as a high-energy laser beam melts loose powder particles. This paper provides multiscale modeling and coordinated control for the SLM of metallic materials including an aluminum (Al)-based alloy (AlSi10Mg), a nickel (Ni)-based super-alloy (Inconel 718), and ceramic particle-reinforced Al-based and Ni-based composites. The migration and distribution mechanisms of aluminium nitride (AlN) particles in SLM-processed Al-based nanocomposites and the in situ formation of a gradient interface between the reinforcement and the matrix in SLM-processed tungsten carbide (WC)/Inconel 718 composites were studied in the microscale. The laser absorption and melting/densification behaviors of AlSi10Mg and Inconel 718 alloy powder were disclosed in the mesoscale. Finally, the stress development during line-by-line localized laser scanning and the parameter-dependent control methods for the deformation of SLM-processed composites were proposed in the macroscale. Multiscale numerical simulation and experimental verification methods are beneficial in monitoring the complicated powder-laser interaction, heat and mass transfer behavior, and microstructural and mechanical properties development during the SLM AM process.

Simultaneous fault detection and control for switched LPV systems with inexact parameters and its application

ABSTRACTThis paper investigates the simultaneous fault detection and control problem for a switched linear parameter-varying (LPV) system. The inexact scheduling parameter-dependent fault detection filters and controllers are designed based on the output framework. To realise the detection and control goals, the inexact scheduling parameter-dependent sufficient LMI conditions are obtained by using multiple Lyapunov functions technique. A mode-dependent average dwell-time switching method is used, which is less strict than the general average dwell-time switching method. Simulation results on an aero-engine model show the feasibility and validity of the designed scheme.

New results on the fourth moment exponentially stable for a class of stochastic nonlinear systems and its application

Under the relaxed triangular-type condition on the drift terms and diffusion terms, this paper investigates the problem of the fourth moment exponentially stable for a class of stochastic nonlinear systems by, respectively, adopting state feedback and output feedback. Based on the Lyapunov stability criterion, the parameter-dependent controller, which is used to compensate for the drift terms and diffusion terms, is constructed such that the closed-loop system is fourth moment exponentially stable. Furthermore, the fourth moment exponential stability of the system states and errors can be guaranteed. Two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.