In the past few years, online convex optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this article, we propose new step-size rules and OCO algorithms that simultaneously exploit gradient predictions, function predictions and dynamics, features particularly pertinent to control applications. The proposed algorithms enjoy static and dynamic regret bounds in terms of the dynamics of the reference action sequence, gradient prediction error, and function prediction error, which are generalizations of known regularity measures from the literature. We present results for both convex and strongly convex costs. We validate the performance of the proposed algorithms in a trajectory tracking case study, as well as portfolio optimization using real-world datasets.

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We study a diagnosis scheme to reliably detect the active mode of discrete-time, switched affine systems in the presence of measurement noise and asynchronous switching. The proposed scheme consists of two parts: (i) the construction of a bank of filters, and (ii) the introduction of a residual/threshold-based diagnosis rule. We develop an exact finite optimization-based framework to numerically solve an optimal bank of filters in which the contribution of measurement noise to the residual is minimized. The design problem is safely approximated through linear matrix inequalities and thus becomes tractable. We further propose a thresholding policy along with probabilistic false-alarm guarantees to estimate the active system mode in real-time. In comparison with the existing results, the guarantees improve from a polynomial dependency in the probability of false alarm to a logarithmic form. This improvement is achieved under the additional assumption of sub-Gaussianity, which is expected in many applications. The performance of the proposed approach is validated through a numerical example and an application of the building radiant system.

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We present a learning method to learn the mapping from an input space to an action space, which is particularly suitable when the action is an optimal decision with respect to a certain unknown cost function. We use an inverse optimization approach to retrieve the cost function by introducing a new loss function and a new hypothesis class of mappings. A tractable convex reformulation of the learning problem is also presented. The method is effective for learning input-action mapping in continuous input-action space with input-output constraints, typically present in control systems. The learning approach can be effectively transformed to learn a Model Predictive Control (MPC) behaviour and a case study to mimic an MPC is presented, which is a rather computationally heavy control strategy. Simulation and experimental results show the effectiveness of the proposed approach.

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We present a learning method to learn the mapping from an input space to an action space, which is particularly suitable when the action is an optimal decision with respect to a certain unknown cost function. We use an inverse optimization approach to retrieve the cost function by introducing a new loss function and a new hypothesis class of mappings. A tractable convex reformulation of the learning problem is also presented. The method is effective for learning input-action mapping in continuous input-action space with input-output constraints, typically present in control systems. The learning approach can be effectively transformed to learn a Model Predictive Control (MPC) behaviour and a case study to mimic an MPC is presented, which is a rather computationally heavy control strategy. Simulation and experimental results show the effectiveness of the proposed approach.

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In this paper, we propose an approach to detect mode transitions and to isolate active modes in discrete-time, switched affine systems. The proposed approach is in particular constructed for systems in which the controller is oblivious of the switching signal. The diagnosis approach consists of two main parts: construction of a bank of output filters (that generate desired residuals) and definition of a certain type of residual/threshold-based diagnosis rules. The filters' construction is cast as linear feasibility problems. These feasibility problems enforce desirable diagnosis relationships between each subsystem's affine constant and each residual. The diagnosis rules are inspired by the well-known generalized observer scheme. Moreover, we provide a method to compute each mode's diagnosis time based on the diagnosis rules and properly chosen residual thresholds. A numerical example is presented to show the performance of the proposed approach.

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In this paper, we propose an event-based sampling policy to implement a constraint-tightening, robust MPC method. The proposed policy enjoys a computationally tractable design and is applicable to perturbed, linear time-invariant systems with polytopic constraints. In particular, the triggering mechanism is suitable for plants with no centralized sensory node as the triggering mechanism can be evaluated locally at each individual sensor. From a geometrical viewpoint, the mechanism is a sequence of hyperrectangles surrounding the optimal state trajectory such that robust recursive feasibility and robust stability are guaranteed. The design of the triggering mechanism is cast as a constrained parametric-in-set optimization problem with the volume of the set as the objective function. Reparameterized in terms of the set vertices, we show that the problem admits a finite tractable convex program reformulation and a linear program relaxation. Several numerical examples are presented to demonstrate the effectiveness and limitations of the theoretical results.

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Treating optimization methods as dynamical systems can be traced back centuries ago in order to comprehend the notions and behaviors of optimization methods. Lately, this mindset has become the driving force to design new optimization methods. Inspired by the recent dynamical system viewpoint of Nesterov's fast method, we propose two classes of fast methods, formulated as hybrid control systems, to obtain prespecified exponential convergence rate. Alternative to the existing fast methods, which are parametric-in-time second-order differential equations, we dynamically synthesize feedback controls in a state-dependent manner. Namely, in the first class, the damping term is viewed as the control input, while in the second class the amplitude with which the gradient of the objective function impacts the dynamics serves as the controller. The objective function requires to satisfy the so-called Polyak-Łojasiewicz inequality, which effectively implies no local optima and a certain gradient-domination property. Moreover, we establish that both hybrid structures possess Zeno-free solution trajectories. We finally provide a mechanism to determine the discretization step size to attain an exponential convergence rate.

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In this paper, an event-triggering approach is proposed for a robust model predictive control method. The approach is applicable to constrained, linear time-invariant systems with bounded, additive disturbances. At each triggering instant, the triggering mechanism is designed online using a linear programming approach. Intuitively, the mechanism is a sequence of hyper-rectangles that surround the optimal state trajectory, over the prediction horizon. Standard analyses of robust feasibility and robust stability of the closed-loop, event-triggered control system are conducted. A numerical example is presented to show benefits of the proposed approach. In particular and under the assumption that the disturbance has a uniform distribution, we further study some statistical properties of the generated triggering instants.

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Event-Triggered control (ETC) implementations have been proposed to overcome the inefficiencies of periodic (time-triggered) controller designs, namely the over-exploitation of the computing and communication infrastructure. However, the potential of aperiodic Event-Triggered techniques to reuse the freed bandwidth, and to reduce energy consumption on wireless settings, has not yet been truly reached. The main limitation to fully exploit ETC’s great traffic reductions lies on the difficulty to predict the occurrence of controller updates, forcing the use of conservative scheduling approaches in practice. Having a model of the timing behaviour of ETC is of paramount importance to enable the construction of model-based schedulers for such systems. Furthermore, on wireless control systems these schedulers allow to tightly schedule listening times, thus reducing energy consumption. In this chapter we describe an approach to model ETC traffic employing ideas from the symbolic abstractions literature. The resulting models of traffic are timed-automata. We also discuss briefly how these models can be employed to automatically synthesize schedulers.

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Ordinary differential equations, and in general a dynamical system viewpoint, have seen a resurgence of interest in developing fast optimization methods, mainly thanks to the availability of well-established analysis tools. In this study, we pursue a similar objective and propose a class of hybrid control systems that adopts a 2nd-order differential equation as its continuous flow. A distinctive feature of the proposed differential equation in comparison with the existing literature is a state-dependent, time-invariant damping term that acts as a feedback control input. Given a user-defined scalar α, it is shown that the proposed control input steers the state trajectories to the global optimizer of a desired objective function with a guaranteed rate of convergence O(e−αt). Our framework requires that the objective function satisfies the so called Polyak–{Ł}ojasiewicz inequality. Furthermore, a discretization method is introduced such that the resulting discrete dynamical system possesses an exponential rate of convergence.@en

In this paper, we propose a framework to design a class of fast gradient-based methods in continuous-time that, in comparison with the existing literature including Nesterov's fast-gradient method, features a state-dependent, time-invariant damping term that acts as a feedback control input. The proposed design scheme allows for a user-defined, exponential rate of convergence for a class of nonconvex, unconstrained optimization problems in which the objective function satisfies the so-called Polyak-Łojasiewicz inequality. Formulating the optimization algorithm as a hybrid control system, a state-feedback input is synthesized such that a desired rate of convergence is guaranteed. Furthermore, we establish that the solution trajectories of the hybrid control system are Zeno-free.

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We consider a control design problem using wireless sensor/actuator networks. Such systems need to operate within the limited resources of available battery life and bandwidth. To address these concerns, we take a model predictive control (MPC) approach for perturbed LTI systems with constraints on the admissible input and state sets. We propose a triggering mechanism (TM) that aims to reduce the number of MPC updates, with the goal to reduce the communication and computation loads. The TM uses trajectories that have been computed at the last update instant and a current measurement to determine whether or not to trigger an update. The TM consists of two parts: 1) inequalities that are functions of the error signal between the observed states and the predicted trajectories, guaranteeing recursive feasibility, and 2) a scalar inequality, that is a function of a weighted version of the value function at the last triggering instant, guaranteeing closed-loop convergence. Numerical simulations demonstrate the effectiveness of our TM in reducing the number of MPC updates, thereby possibly reducing the communication load as well.

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Unnecessary communication and computation in the periodic execution of control tasks lead to over-provisioning in hardware design (or underexploitation in hardware utilization) in control applications, in particular in networked control systems.
To address these issues, researchers have proposed a new class of strategies, named event-driven strategies. Despite their beneficiary effects, matters like task scheduling and appropriate dimensioning of communication components have become more complicated with respect to traditional periodic strategies. In
this paper, we present a formal approach to derive an abstracted system that captures the sampling behavior of a family of eventtriggered strategies for the case of LTI systems. This structure approximately simulates the sampling behavior of the aperiodic control system. Furthermore, the resulting abstract system is equivalent to a timed safety automaton. In the construction of
the abstraction, the state space is confined to a finite number of convex regions, each of which represents a mode in the quotient system. An LMI-based technique is deployed to derive a sampling time interval associated to each region. Finally, reachability analysis is leveraged to find the transitions of the abstract system.@en

In networked control systems, the advent of event-triggering strategies in the sampling process has resulted in the usage reduction of network capacities, such as communication bandwidth. However, the aperiodic nature of sampling periods generated by event-triggering strategies has hindered the schedulability of such networks. In this study, we propose a framework to construct a timed safety automaton that captures the sampling behavior of perturbed LTI systems with an L₂-based triggering mechanism proposed in the literature. In this framework, the state-space is partitioned into a finite number of convex polyhedral cones, each cone representing a discrete mode in the abstracted automaton. Adopting techniques from stability analysis of retarded systems accompanied with a polytopic embedding of time, LMI conditions to characterize the sampling interval associated with each region are derived. Then, using reachability analysis, the transitions in the abstracted automaton are derived.

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Distinct advantages of the combination of the pneumatic actuated plants with “on/off” solenoid valves have motivated many researchers to conduct research in this scope. Pulse-width modulation (PWM) is a tool to use such combination in servo tasks. This paper studies the most frequent and well-reported PWM schemes. These PWM schemes have been applied for positioning tasks of the pneumatic actuators using solenoid on/off valves. In this study, the positioning performance of the servo pneumatic system, utilizing different PWM schemes, is investigated through several experiments with step and sinusoidal reference inputs. Rise time, overshoot, and steady-state error, in step input tests, and tracking performance in sinusoidal tests demonstrate the effectiveness of the deployed PWM schemes in the pneumatic system behaviors. Moreover, the closed-loop results demonstrate that the system robustness against the increase of the system’s mass is associated with the applied PWM scheme. Based on the open-loop results, two factors are found to be affecting PWM schemes performance, namely, the difference in the cross-sectional areas on each side of the piston and the piston position, in which these factors have not been considered in the design procedure of the former studies. Taking into account the former factor, a modified version of the PWM schemes is proposed. Steady-state errors in closed-loop tests verify the effectiveness of the developed modified PWM schemes.

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