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This article develops a control method for linear time-invariant systems subject to time-varying and a priori unknown cost functions, that satisfies state and input constraints, and is robust to exogenous disturbances. To this end, we combine the online convex optimization framework with a reference governor and a constraint tightening approach. The proposed framework guarantees recursive feasibility and robust constraint satisfaction. Its closed-loop performance is studied in terms of its dynamic regret, which is bounded linearly by the variation of the cost functions and the magnitude of the disturbances. The proposed method is illustrated by a numerical case study of a tracking control problem.
The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can be developed with capabilities that are unprecedented by classical computers. However, the experimental realization of quantum devices is an active field of research with enormous open challenges, including robustness against noise and scalability. While systems and control theory plays a crucial role in tackling these challenges, the principles of quantum physics lead to a (perceived) high entry barrier for entering the field of quantum computing. This tutorial paper aims at lowering the barrier by introducing basic concepts required to understand and solve research problems in quantum systems. First, we introduce fundamentals of quantum algorithms, ranging from basic ingredients such as qubits and quantum logic gates to prominent examples and more advanced concepts, e.g., variational quantum algorithms. Next, we formalize some engineering questions for building quantum devices in the real world, which requires the careful manipulation of micro
Safety is one of the most important properties of control systems. Sensor faults and attacks and actuator failures may cause errors in the sensor measurements and system dynamics, which leads to erroneous control inputs and hence safety violations. In this paper, we improve the robustness against sensor faults and actuator failures by proposing a class of Fault-Tolerant Control Barrier Functions (FT-CBFs) for nonlinear systems. Our approach maintains a set of state estimators according to fault patterns and incorporates CBF-based linear constraints for each state estimator. We then propose a framework for joint safety and stability by integrating FT-CBFs with Control Lyapunov Functions. With a similar philosophy of utilizing redundancy, we proposed High order CBF-based approach to ensure safety when actuator failures occur. We propose a sum-of-squares (SOS) based approach to verify the feasibility of FT-CBFs for both sensor faults and actuator failures. We evaluate our approach via two case studies, namely, a wheeled mobile robot (WMR) system in the presence of a sensor attack and a Boeing 747 lateral control system under actuator failures.
The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed orbits on a constraint manifold. A desired orbit is selected on the manifold and a Poincare section is constructed at a fixed point on the orbit. The corresponding Poincare map is linearized about the fixed point; this results in a discrete linear time-invariant system. To stabilize the desired orbit, impulsive inputs are applied when the system trajectory crosses the Poincare section; these inputs can be designed using standard techniques such as LQR. The Impulse Controlled Poincare Map (ICPM) based control design has lower complexity and computational cost than control designs proposed earlier. The generality of the ICPM approach is demonstrated using the 2-DOF cart-pendulum and the 3-DOF tiptoebot.
Cloud computing and distributed computing are becoming ubiquitous in many modern control systems such as smart grids, building automation, robot swarms or intelligent transportation systems. Compared to "isolated" control systems, the advantages of cloud-based and distributed control systems are, in particular, resource pooling and outsourcing, rapid scalability, and high performance. However, these capabilities do not come without risks. In fact, the involved communication and processing of sensitive data via public networks and on third-party platforms promote, among other cyberthreats, eavesdropping and manipulation of data. Encrypted control addresses this security gap and provides confidentiality of the processed data in the entire control loop. This paper presents a tutorial-style introduction to this young but emerging field in the framework of secure control for networked dynamical systems.
In this paper, we present a state-feedback controller design method for bilinear systems. To this end, we write the bilinear system as a linear fractional representation by interpreting the state in the bilinearity as a structured uncertainty. Based on that, we derive convex conditions in terms of linear matrix inequalities for the controller design, which are efficiently solvable by semidefinite programming. Further, we prove asymptotic stability and quadratic performance of the resulting closed-loop system locally in a predefined region. The proposed design uses gain-scheduling techniques and results in a state feedback with rational dependence on the state, which can substantially reduce conservatism and improve performance in comparison to a simpler, linear state feedback. Moreover, the design method is easily adaptable to various scenarios due to its modular formulation in the robust control framework. Finally, we apply the developed approaches to numerical examples and illustrate the benefits of the approach.
This paper addresses the challenge of network synchronization under limited communication, involving heterogeneous agents with different dynamics and various network topologies, to achieve consensus. We investigate the distributed adaptive control for interconnected unknown linear subsystems with a leader and followers, in the presence of input-output disturbance. We enhance the communication within multi-agent systems to achieve consensus under the leadership's guidance. While the measured variable is similar among the followers, the incoming measurements are weighted and constructed based on their proximity to the leader. We also explore the convergence rates across various balanced topologies (Star-like, Cyclic-like, Path, Random), featuring different numbers of agents, using three distributed algorithms, ranging from first- to high-order tuners to effectively address time-varying regressors. The mathematical foundation is rigorously presented from the network designs of the unknown agents following a leader, to the distributed methods. Moreover, we conduct several numerical simulations across various networks, agents and tuners to evaluate the effects of sparsity in the interac
Projected Dynamical Systems (PDSs) form a class of discontinuous constrained dynamical systems, and have been used widely to solve optimization problems and variational inequalities. Recently, they have also gained significant attention for control purposes, such as high-performance integrators, saturated control and feedback optimization. In this work, we establish that locally Lipschitz continuous dynamics, involving Control Barrier Functions (CBFs), namely CBF-based dynamics, approximate PDSs. Specifically, we prove that trajectories of CBF-based dynamics uniformly converge to trajectories of PDSs, as a CBF-parameter approaches infinity. Towards this, we also prove that CBF-based dynamics are perturbations of PDSs, with quantitative bounds on the perturbation. Our results pave the way to implement discontinuous PDS-based controllers in a continuous fashion, employing CBFs. We demonstrate this on numerical examples on feedback optimization and synchronverter control. Moreover, our results can be employed to numerically simulate PDSs, overcoming disadvantages of existing discretization schemes, such as computing projections to possibly non-convex sets. Finally, this bridge between
This article presents a sparse, low-memory footprint optimization algorithm for the implementation of the model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard MPC formulations, such as an increased domain of attraction and guaranteed recursive feasibility even in the event of a sudden reference change. However, this comes at the expense of the addition of a small amount of decision variables to the MPC's optimization problem that complicates the structure of its matrices. We propose a sparse optimization algorithm, based on an extension of the alternating direction method of multipliers, that exploits the structure of this particular MPC formulation. We describe the controller formulation and detail how its structure is exploited by means of the aforementioned optimization algorithm. We show closed-loop simulations comparing the proposed solver against other solvers and approaches from the literature.
In this paper, we study the relationship between systems controlled via Control Barrier Function (CBF) approaches and a class of discontinuous dynamical systems, called Projected Dynamical Systems (PDSs). In particular, under appropriate assumptions, we show that the vector field of CBF-controlled systems is a Krasovskii-like perturbation of the set-valued map of a differential inclusion, that abstracts PDSs. This result provides a novel perspective to analyze and design CBF-based controllers. Specifically, we show how, in certain cases, it can be employed for designing CBF-based controllers that, while imposing safety, preserve asymptotic stability and do not introduce undesired equilibria or limit cycles. Finally, we briefly discuss about how it enables continuous implementations of certain projection-based controllers, that are gaining increasing popularity.
IR (Infra-Red) detectors are widely used in Space-borne remote sensing satellites. In order to achieve a high signal to noise ratio, the IR detectors need to be operated at cryogenic temperatures. Traditionally, the cryogenic cooling of these detectors is achieved using passive cooling techniques. However recent trend is to employ Stirling-cycle based miniaturized active cryocoolers. An accurate and stringent control of active cryocooler cold-tip temperature is essential to accomplish high signal & image quality from the IR detectors. This paper presents work on investigations and comparison of performance of proposed 2-DOF (2-Degrees-of-Freedom) versus traditional 1-DOF feedback-control structures for the control of cryocooler cold-tip temperature used in IR (Infra-Red) detectors of Space Satellites. Towards this, first-principle based control oriented mathematical model simulated in Matlab/Simulink is proposed to support such investigation and controller tuning. Open-loop (system) and closed-loop (controls) simulation results are tuned & validated with the experimental data obtained from the Lab-scale test-setup of a commercial Stirlingcryocooler. The performance of 2-DOF
In this paper, we propose a novel controller design approach for unknown nonlinear systems using the Koopman operator. In particular, we use the recently proposed stability- and feedback-oriented extended dynamic mode decomposition (SafEDMD) architecture to generate a data-driven bilinear surrogate model with certified error bounds. Then, by accounting for the obtained error bounds in a controller design based on the bilinear system, one can guarantee closed-loop stability for the true nonlinear system. While existing approaches over-approximate the bilinearity of the surrogate model, thus introducing conservatism and providing only local guarantees, we explicitly account for the bilinearity by using sum-of-squares (SOS) optimization in the controller design. More precisely, we parametrize a rational controller stabilizing the error-affected bilinear surrogate model and, consequently, the underlying nonlinear system. The resulting SOS optimization problem provides explicit data-driven controller design conditions for unknown nonlinear systems based on semidefinite programming. Our approach significantly reduces conservatism by establishing a larger region of attraction and improved
Research on fault diagnosis on highly nonlinear dynamic systems such as the engine of a vehicle have garnered huge interest in recent years, especially with the automotive industry heading towards self-driving technologies. This article presents a novel opensource simulation testbed of a turbocharged spark ignited (TCSI) petrol engine system for testing and evaluation of residuals generation and fault diagnosis methods. Designed and developed using Matlab/Simulink, the user interacts with the testbed using a GUI interface, where the engine can be realistically simulated using industrial-standard driving cycles such as the Worldwide harmonized Light vehicles Test Procedures (WLTP), the New European Driving Cycle (NEDC), the Extra-Urban Driving Cycle (EUDC), and EPA Federal Test Procedure (FTP-75). The engine is modeled using the mean value engine model (MVEM) and is controlled using a proportional-integral (PI)-based boost controller. The GUI interface also allows the user to induce one of the 11 faults of interest, so that their effects on the performance of the engine are better understood. This minimizes the risk of causing permanent damages to the engine and shortening its lifes
Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of operation, the system must maintain adequate disturbance rejection capability at the time scales of both rotor angle and system frequency dynamics. This calls for flexibility to be exploited on both the generation and demand sides, compensating volatility and ensuring stability at the two separate time scales. This article proposes a hierarchical power flow control architecture that involves both transmission and distribution networks as well as individual buildings to enhance both small-signal rotor angle stability and frequency stability of the transmission network. The proposed architecture consists of a transmission-level optimizer enhancing system damping ratios, a distribution-level controller following transmission commands and providing frequency support, and a building-level scheduler accounting for quality of service and following the distribution-level targets. We validate the feasibility and performance of the whole control architecture through real-time hardware-in-lo
We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible solution within a finite number of iterations, using primal averaging and a constraint tightening approach. The primal update is performed in a distributed way and does not require exact solutions, while the dual problem uses an approximate subgradient method. Stability of the scheme is established using bounded suboptimality.
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic constraints, mechanical systems with symmetry and mechanical systems evolving on semidirect products. We introduce the notions of linear connection, symmetric product and geodesically invariant subbundle on a Lie algebroid. We present appropriate tests for various notions of accessibility and controllability, and analyze the relation between the controllability properties of control systems related by a morphism of Lie algebroids.
As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While the Bayesian approaches prevalent for safety-critical applications usually rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and the latent state, making the quantification of uncertainties and the design of controllers with formal performance guarantees considerably more challenging. This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states based on a combination of particle Markov chain Monte Carlo methods and scenario theory. Probabilistic performance guarantees are derived for the resulting input trajectory, and an approach to validate the performance of arbitrary control laws is presented. The effectiveness of the proposed method is demonstrated in a numerical simulation.
We present a safety-critical controller for the problem of stabilization for force-controlled nonholonomic mobile robots. The proposed control law is based on the constructions of control Lyapunov functions (CLFs) and control barrier functions (CBFs) for cascaded systems. To address nonholonomicity, we design the nominal controller that guarantees global asymptotic stability and local exponential stability for the closed-loop system in polar coordinates and construct a strict Lyapunov function valid on any compact sets. Furthermore, we present a procedure for constructing CBFs for cascaded systems, utilizing the CBF of the kinematic model through integrator backstepping. Quadratic programming is employed to combine CLFs and CBFs to integrate both stability and safety in the closed loop. The proposed control law is time-invariant, continuous along trajectories, and easy to implement. Our main results guarantee both safety and local asymptotic stability for the closed-loop system.
Off-road driving operations can be a challenging environment for human conductors as they are subject to accidents, repetitive and tedious tasks, strong vibrations, which may affect their health in the long term. Therefore, they can benefit from a successful implementation of autonomous vehicle technology, improving safety, reducing labor costs and fuel consumption, and increasing operational efficiency. The main contribution of this paper is the experimental validation of a path tracking control strategy, composed of longitudinal and lateral controllers, on an off-road scenario with a fully-loaded heavy-duty truck. The longitudinal control strategy relies on a Non-Linear Model Predictive Controller (NMPC), which considers the path geometry and simplified vehicle dynamics to compute a smooth and comfortable input velocity, without violating the imposed constraints. The lateral controller is based on a Robust Linear Quadratic Regulator (RLQR), which considers a vehicle model subject to parametric uncertainties to minimize its lateral displacement and heading error, as well as ensure stability. Experiments were carried out using a fully-loaded vehicle on unpaved roads in an open-pit