Robust Control Approach Research Articles

Epistemology of voltage control in DER-rich power system

Despite the recent development of several scalable, robust, and resilient control approaches with superior convergence properties considering an increasing penetration of distributed energy resources (DERs), cognitive oversights often simplify several aspects of the cyber–physical power system in the controller development. Following the identification of the limitations of classical controller definitions, we justify alternative definitions of voltage control approaches classifiers considering three inter-disciplinary domains: (i) power system, (ii) optimization and decision-making, and (iii) networking and cyber-security, to develop a taxonomy for helping in real-world comparative performance analysis and deployability of these controllers. We observe that classical and introduced domain-based definitions together can better classify the control algorithms.

Robust Constraint-Following Control for Uncertain Mechanical Systems With Generalized Udwadia-Kalaba Approach

In this letter, we propose a robust constraint-following control approach for uncertain mechanical systems under both equality and inequality constraints. Particularly, both the global and local inequality constraints are systematically incorporated into the Udwadia-Kalaba (U-K) equation leveraging the diffeomorphism technique, wherein a novel smooth approximation of the local inequality constraints is proposed to address the non-differentiability resulting from its spatiotemporal dependence nature. Based on this development, the generalized U-K equation is mathematically established. With this, we develop a robust constraint-following control strategy to ensure satisfying system performance in the presence of uncertainties and various constraints. Moreover, by Lyapunov minimax approach, the proposed control strategy guarantees both uniform boundedness (UB) and uniform ultimate boundedness (UUB) of the system. Finally, numerical simulations on the lateral motion control of an autonomous vehicle demonstrate the effectiveness of the proposed approach.

Robust Variable Structure Control Approach of Two Series-Connected Five-Phase PMSMs Under Healthy and Faulty Operation Modes

Robust Variable Structure Control Approach of Two Series-Connected Five-Phase PMSMs Under Healthy and Faulty Operation Modes

SPOCK: A proximal method for multistage risk-averse optimal control problems

Risk-averse optimal control problems have gained a lot of attention in the last decade, mostly due to their attractive mathematical properties and practical importance. They can be seen as an interpolation between stochastic and robust optimal control approaches, allowing the designer to trade-off performance for robustness and vice-versa. Due to their stochastic nature, risk-averse problems are of a very large scale, involving millions of decision variables, which poses a challenge in terms of efficient computation. In this work, we propose a splitting for general risk-averse problems involving linear dynamical systems and show how to efficiently compute iterates on a GPU-enabled hardware. Moreover, we propose Spock — a new algorithm that utilizes the proposed splitting and takes advantage of the SuperMann scheme combined with fast directions from Anderson's acceleration method for enhanced convergence speed. We implement Spock in Julia as an open-source solver, which is amenable to warm-starting and massive parallelization.

Robust Control of Cascaded H-Bridge Multilevel Inverters for Grid-Tied PV Systems Subject to Faulty Conditions

This paper deals with the design and implementation of a robust control approach for grid-tied PV systems. The main controller’s objectives are to inject the maximum available power to the grid, whilst guaranteeing power quality even under faulty conditions. To this end, a multi-loop regulator is designed for the Cascaded H-Bridge Multilevel Inverters (CHBMIs) by combining a sliding mode control strategy for maximum power point tracking and a Lyapunov approach for Power Factor Correction (PFC). Validation of the proposed approach using Matlab/ SimPowerSimscape environment confirmed the ability of the proposed approach to successfully accomplish its objectives in terms of references tracking and regulation under both matching and mismatching irradiation levels as well as faulty modes stemming from the photovoltaic (PV) panels and/or the dc-dc converters. Additionally, the proposed approach was shown to outperform conventional approaches and enable the continuous operation of the PV system under various failure modes affecting multiple PV panels and/or their associated dc-dc boost converters.

Stochastic Model Predictive Control With a Safety Guarantee for Automated Driving

Automated vehicles require efficient and safe planning to maneuver in uncertain environments. Largely this uncertainty is caused by other traffic participants, e.g., surrounding vehicles. Future motion of surrounding vehicles is often difficult to predict. Whereas robust control approaches achieve safe, yet conservative motion planning for automated vehicles, Stochastic Model Predictive Control (SMPC) provides efficient planning in the presence of uncertainty. Probabilistic constraints are applied to ensure that the maximal risk remains below a predefined level. However, safety cannot be ensured as probabilistic constraints may be violated, which is not acceptable for automated vehicles. Here, we propose an efficient trajectory planning framework with safety guarantees for automated vehicles. SMPC is applied to obtain efficient vehicle trajectories for a finite horizon. Based on the first optimized SMPC input, a guaranteed safe backup trajectory is planned using reachable sets. This backup is used to overwrite the SMPC input if necessary for safety. Recursive feasibility of the safe SMPC algorithm is proved. Highway simulations show the effectiveness of the proposed method regarding performance and safety.

Robust homography-based visual servo control for a quadrotor UAV tracking a moving target

In this study, a new robust homography-based visual tracking control approach for the quadrotor unmanned aerial vehicle (UAV) is developed. Specifically, employing the homography matrix as feedback, a hierarchical homography-based visual servoing (HBVS) scheme with a new command attitude extraction method to account for the underactuation of UAV is proposed. On this basis, a smooth hyperbolic tangent function is fulfilled as an augmented part of the backstepping control scheme, which guarantees the non-negative total thrust and avoid singularity. Additionally, a cascaded filter-based estimator and adaptive laws with integrable functions are embedded to counteract uncertainties including external perturbations, unknown acceleration of the moving target, and unknown image depth, and to facilitate the system’s asymptotic stability simultaneously. The theoretical analysis testifies that the whole close-loop system is asymptotically stable. Simulations further verify that the proposed HBVS controller can realize the visual tracking with a superior performance.

Practical robust control design and experimental validation of modular jointed cooperative robots with inequality constraints

In this paper, a new practical dynamic robust control approach for cooperative robots with inequality constraints is proposed. The controller can compensate errors caused by uncertainties and external disturbances. The inequality constraint is eliminated by choosing proper boundary function and using state transformation. In this way, the controlled output is guaranteed within the desired range. The Lyapunov minimax method is used to prove that the controller can guarantee the uniform boundedness and uniform ultimate boundedness and stability of the robot system. Experimental verifications are carried out on a 2-DOF cooperative robot experimental platform with joint modules. The experimental platform is equipped with a rapid prototyping controller system (CSPACE). Numerical simulation and experimental verification results show that the proposed practical robust controller has significant advantages of trajectory tracking performance and security for cooperative robots with inequality constraints.

Contraction-based model predictive control for stochastic nonlinear discrete-time systems with time-varying delays via multi-dimensional Taylor network

For stochastic nonlinear systems with time-varying delays, the existing robust control approaches are unnecessarily conservative in most practical scenarios. Within this context, a mathematically rigorous and computationally tractable tube-based model predictive control scheme is proposed in the framework of contraction theory. A contraction metric is systematically constructed via convex optimization by forming a differential LyapunovKrasovskii function on tangent space. It guarantees the perturbed actual solution trajectories to be contained within a robust positive invariant tube centered along the reference trajectories and results in an explicit exponential bound on the deviation. The application scenarios of the control contraction metric controller are extended from constant delay systems into time-varying delay systems thereby. Compared with the existing robust mechanism for time-delay systems based on min-max optimization formulation with a linear feedback controller, the proposed scheme greatly reduces the design conservativeness and yields a larger region of attraction. A sparse multi-dimensional Taylor network (MTN) is designed to parameterize the family of the geodesic. Compared to conventional NNs and MTN surrogates, sparse MTN features a more concise topology that enhances its computational efficiency conspicuously. Results of the numerical simulations verify the effectiveness of the proposed method.

A novel approach for robust model predictive control applied to switched linear systems through state and output feedback

This paper proposes a robust switched model-based predictive controller design for discrete linear systems with state constraints, inputs, and disturbances limited in norm. Modeled via linear matrix inequalities, the online and offline designs of the proposed control aim at minimizing the upper bound of the quadratic performance index for a horizon of infinite prediction associated with the state estimator and the switching rule, seeking to guarantee the robust stability for closed-loop systems. To this end, three theorems are formulated. To demonstrate the effectiveness of the control strategy, a comparative analysis is performed between the performance of the proposed model and a benchmark method. From the results, it is possible to conclude that the proposed method is promising in the scope of control of linear systems subject to switching, being more efficient than the benchmark for the stabilization and control of both numerical examples.

The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional order has been developed to construct the control strategy of the abovementioned sliding mode by employing the structure of nonlinear fractional PID (NLPID) controllers. The suggested control mechanism using Lyapunov’s theorem developed robust adaptive rules in such a way that the estimation error of the system’s unknown parameters and time delays tends to be zero. Furthermore, the proposed robust control approach’s stability has been demonstrated using Lyapunov stability criteria and Lipschitz conditions. Then, in order to assess the performance of the proposed mechanism, the presented control approach was used to simulate the synchronization of two chaotic jerk systems with uncertainty, unknown time delays, and external distortion. The results of the simulation confirm the robust and desirable synchronization performance. Finally, a secure communications mechanism based on the proposed technique is shown as a practical implementation of the introduced control strategy, in which the message signal is disguised in the transmitter with high security and well recovered in the receiver with high quality, according to the mean squared error (MES) criteria.

Designing a resilient supply chain through a robust adaptive model predictive control policy under perishable goods and uncertain forecast information

We consider the inventory control problem for Supply Chains (SC) with deteriorating items and an uncertain future customer demand freely varying inside a given compact set. The problem is to define a resilient Replenishment Policy (RP) keeping the actual inventory level as close as possible to a desired reference trajectory. This requirement should be satisfied despite uncertainties on the decay factor of stocked goods and unexpected customer demand patterns outside the bounds of the compact set. We propose a method based on a Resilient Robust Model Predictive Control (RRMPC) approach. This requires dealing with a Min-Max Constrained Optimization Problem (MMCOP). To reduce the numerical complexity of the algorithm, the control signal is parametrized using B-spline functions.

Using a Reduced Order Robust Control Approach to Damp Subsynchronous Resonance in Power Systems

his work focuses on the use of the Linear Quadratic Gaussian (LQG) technique to construct a reliable Static VAr Compensator (SVC), Thyristor Controlled Series Compensator (TCSC), and Excitation System controller for damping Subsynchronous Resonance ( SSR ) in a power system. There is only one quantifiable feedback signal used by the controller (generator speed deviation). It is also possible to purchase this controller in a reduced-order form. The findings of the robust control are contrasted with those of the “idealistic” full state optimal control. The LQG damping controller’s regulator robustness is then strengthened by the application of Loop Transfer Recovery (LTR). Nonlinear power system simulation is used to confirm the resilience of the planned controller and demonstrates how well the regulator dampens power system oscillations. The approach dampens all torsional oscillatory modes quickly while maintaining appropriate control actions, according to simulation results.

Robust control of discrete minimum and non‐minimum phase systems via data‐driven virtual reference feedback tuning and IMC

AbstractIn this paper, we develop a novel robust control approach for discrete minimum and non‐minimum phase systems via a combined data‐driven virtual reference feedback tuning () and internal model control (IMC) scheme. The first step in the conventional method controller design is the selection of the closed‐loop reference model (), and selection is still an open problem. The integration of the scheme and the VRFT method provides the advantage of flexibility in controller design due to the incorporation of the filter. As a result, the proposed design method begins with the selection of and filter. Unlike the standard method, the proposed combined and design approach has the unique feature of taking into account a robustness property of dynamics, namely, maximum sensitivity () as the design specification for the and IMC filter selection. Moreover, the proposed approach includes a robustness specification that resolves the trade‐off between performance and robustness in real‐time controller design. Furthermore, the robustness guarantee with plant uncertainties and controller fragility is elucidated. The proposed approach is validated using numerical simulations and experimental validation through the temperature control process. Compared to conventional controllers, experimental and simulation results show that the proposed controllers have less tracking error, minimize control effort, and improve robustness.

An adaptive hybrid control strategy for a class of nonlinear systems

This study provides an adaptive fuzzy control scheme for the class of nonlinear uncertain strict-feedback systems with external disturbances. The backstepping and synergetic control theories are used to develop a robust control approach for this class of systems. The unknown behaviors of the system are estimated through fuzzy systems. The stability is analyzed using the Lyapunov method, which shows that the proposed control method ensures that all the signals of the closed-loop system are bounded, and the tracking error converges approximately to zero. Two simulation examples are given to demonstrate the efficiency of the developed control approach.

Robust Adaptive Learning-Based Path Tracking Control of Autonomous Vehicles Under Uncertain Driving Environments

This paper investigates the path tracking control problem of autonomous vehicles subject to modelling uncertainties and external disturbances. The problem is approached by employing a 2-degree of freedom vehicle model, which is reformulated into a newly defined parametric form with the system uncertainties being lumped into an unknown parametric vector. On top of the parametric system representation, a novel robust adaptive learning control (RALC) approach is then developed, which estimates the system uncertainties through iterative learning while treating the external disturbances by adopting a robust term. It is shown that the proposed approach is able to improve the lateral tracking performance gradually through learning from previous control experiences, despite only partial knowledge of the vehicle dynamics being available. It is noteworthy that a novel technique targeting at the non-square input distribution matrix is employed so as to deal with the under-actuation property of the vehicle dynamics, which extends the adaptive learning control theory from square systems to non-square systems. Moreover, the convergence properties of the RALC algorithm are analysed under the framework of Lyapunov-like theory by virtue of the composite energy function and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> -norm. The effectiveness of the proposed control scheme is verified by representative simulation examples and comparisons with existing methods.

Deep Q‐learning: A robust control approach

AbstractThis work aims at constructing a bridge between robust control theory and reinforcement learning. Although, reinforcement learning has shown admirable results in complex control tasks, the agent's learning behavior is opaque. Meanwhile, system theory has several tools for analyzing and controlling dynamical systems. This article places deep Q‐learning is into a control‐oriented perspective to study its learning dynamics with well‐established techniques from robust control. An uncertain linear time‐invariant model is formulated by means of the neural tangent kernel to describe learning. This novel approach allows giving conditions for stability (convergence) of the learning and enables the analysis of the agent's behavior in frequency‐domain. The control‐oriented approach makes it possible to formulate robust controllers that inject dynamical rewards as control input in the loss function to achieve better convergence properties. Three output‐feedback controllers are synthesized: gain scheduling , dynamical , and fixed‐structure controllers. Compared to traditional deep Q‐learning techniques, which involve several heuristics, setting up the learning agent with a control‐oriented tuning methodology is more transparent and has well‐established literature. The proposed approach does not use a target network and randomized replay memory. The role of the target network is overtaken by the control input, which also exploits the temporal dependency of samples (opposed to a randomized memory buffer). Numerical simulations in different OpenAI Gym environments suggest that the controlled learning can converge faster and receive higher scores (depending on the environment) compared to the benchmark double deep Q‐learning.

Robust Output Regulation for a Constrained Omnidirectional Mobile Robot

This paper aims to design a robust output control to regulate the output for an uncertain omnidirectional mobile robot with input saturation and state constraints, in the presence of external disturbances. The proposed robust control approach is composed of a linear control part, that is designed based on the attractive ellipsoid method and a barrier Lyapunov function approach, taking into account the input and state constraints, and a nonlinear control part that can compensate the effect of matched disturbances. The synthesis of the robust control is given in terms of linear matrix inequalities. Simulation results show the workability of the proposed robust control approach.

Distributed Control of Parallel DC–DC Converters Under FDI Attacks on Actuators

The parallel connection of DC-DC converters requires the development of an appropriate control strategy that regulates load voltage and shares current amongst participating converters. This paper proposes a resilient and robust cooperative distributed control approach that simultaneously ensures voltage regulation and balanced current sharing in parallel DC-DC converters in the presence of false data injection attacks on control input channels. Based on analytical tools from network control and Lyapunov stability theory, concise stability certificates are derived. The proposed cooperative distributed control strategy guarantees resilience against unknown bounded attacks on the actuators of DC-DC converters and the robustness to uncertainties in load parameters and the physical parameters of converters. Furthermore, the control design for each converter does not require any knowledge about the number of participating converters. The detailed simulation and experimental results verify the satisfactory performance of the proposed method in voltage regulation and balanced current sharing in parallel converters, as well as resilience to bounded false data injection attacks.

Robust deadlock control in automated manufacturing systems with unreliable resources based on an algebraic way

In automated manufacturing systems (AMSs), because of unpredictable failures, resources can lose functions such that the deadlock control methods, in existence, are invalidated. In this paper, a robust deadlock control approach is proposed for AMSs with multiple unreliable resources. The considered AMSs modelled by Petri nets (PNs) allow to acquire different types of resources at each processing stage. In order to visualise the fact that resource failures occur in AMSs, recovery subnets are designed for the modelling AMSs to depict the failures and recoveries of resources. Based on a siphon detection method performed by a set of integer linear programming formulations, a control specification is proposed. Control places (monitors) with their control variables are designed for the detected unmarked siphons at a marking to guarantee that they are always marked even if some unreliable resources break down. Iteratively, all unmarked siphons are detected and controlled. Therefore, a robust deadlock supervisor is synthesised to ensure the controlled system's liveness no matter there exist resource failures or not. The theoretical analyses and proof are given to verify the correctness of the proposed method. Finally, the comparative studies are presented to expound the proposed method's effectiveness and efficiency.