Self-triggered control (STC) and periodic event-triggered control (PETC) are aperiodic sampling techniques aiming at reducing control data communication when compared to periodic sampling. In both techniques, the effects of measurement noise in continuous-time systems with output feedback are unaddressed. In this work we prove that additive noise does not hinder stability of output-feedback PETC of linear time-invariant (LTI) systems. Then we build an STC strategy that estimates PETC's worst-case triggering times. To accomplish this, we use set-based methods, more specifically ellipsoidal sets, which describe uncertainties on state, disturbances and noise. Ellipsoidal reachability is then used to predict worst-case triggering condition violations, ultimately determining the next communication time. The ellipsoidal state estimate is recursively updated using guaranteed state estimation (GSE) methods. The proposed STC is designed to be computationally tractable at the expense of some added conservatism. It is expected to be a practical STC implementation for a broad range of applications.
Resilient systems are able to recover quickly and easily from disturbed system states that might result from hazardous events or malicious attacks. In this paper a novel resilience metric for linear time invariant systems is proposed: the minimum control energy required to disturb the system is set into relation to the minimum control energy needed to recover. This definition extends known disturbance rejection metrics considering random effects to account for adversarial disturbances. The worst-case disturbance and the related resilience index can be computed efficiently via solving a general…
We propose a method for open-loop stochastic optimal control of LTI systems based on Taylor approximations of quantile functions. This approach enables efficient computation of quantile functions that arise in chance constrained reformulations. We are motivated by multi-vehicle planning problems for LTI systems with norm-based collision avoidance constraints, and polytopic feasibility constraints. Respectively, these constraints can be posed as reverse-convex and convex chance constraints that are affine in the control and disturbance. We show for constraints of this form, piecewise affine app…
Predicting the state of a system in a relatively near future time instant is often needed for control purposes. However, when the system is affected by external disturbances, its future state is dependent on the forthcoming disturbance; which is, in most of the cases, unknown and impossible to measure. In this scenario, making predictions of the future system-state is not straightforward and, indeed, there are scarce contributions provided to this issue. This paper treats the following problem: given a LTI system affected by continuously differentiable unknown disturbances, how its future stat…
This paper addresses finite-time horizon optimal control of single-loop networked control systems with stochastically modeled communication channel and disturbances. To cope with the uncertainties, an optimization-based control scheme is proposed which uses a disturbance feedback and the age of information as central aspects. The disturbance feedback is an extension of the control law used for balanced stochastic optimal control previously proposed for control systems without network. Balanced optimality is understood as a compromise between minimizing of expected deviations from the reference…
A powerful result from behavioral systems theory known as the fundamental lemma allows for predictive control akin to Model Predictive Control (MPC) for linear time invariant (LTI) systems with unknown dynamics purely from data. While most of data-driven predictive control literature focuses on robustness with respect to measurement noise, only few works consider exploiting probabilistic information of disturbances for performance-oriented control as in stochastic MPC. In this work, we propose a novel data-driven stochastic predictive control scheme for chance-constrained LTI systems subject t…
While many techniques have been developed for chance constrained stochastic optimal control with Gaussian disturbance processes, far less is known about computationally efficient methods to handle non-Gaussian processes. In this paper, we develop a method for solving chance constrained stochastic optimal control problems for linear time-invariant systems with general additive disturbances with finite moments and unimodal chance constraints. We propose an open-loop control scheme for multi-vehicle planning, with both target sets and collision avoidance constraints. Our method relies on the one-…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is reformulated as a parameter estimation problem. In contrast with existing results our solution achieves convergence in finite-time, without injection of high gain, and imposes very weak assumptions on the communication graph---namely the existence of a Hamiltonian walk. The scheme is shown to be robust vis-á-vis external disturbances and communication delays.
This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group exchanges locally-computed framers or interval-valued state estimates with neighbors, and coordinates its update via an intersection operation. We show that the proposed framers are guaranteed to bound the true state trajectory of the system by construction, i.e., without imposing any additional assumptions or constraints. Moreover, we provide necessary and sufficient condition…
Previously, we derived exact relationships between the properties of a linear time-invariant control system and properties of an anomaly detector that quantified the impact an attacker can have on the system if that attacker aims to remain stealthy to the detector. A necessary first step in this process is to be able to precisely tune the detector to a desired level of performance (false alarm rate) under normal operation, typically through the selection of a threshold parameter. To-date efforts have only considered Gaussian noises. Here we generalize the approach to tune a chi-squared anomaly…
Design of optimal repetitive control based on EID estimator with adaptive periodic event-triggered mechanism for linear systems subjected to exogenous disturbances
This work develops a data-based construction of inverse dynamics for LTI systems. Specifically, the problem addressed here is to find an input sequence from the corresponding output sequence based on pre-collected input and output data. The problem can be considered as a reverse of the recent use of behavioral approach, in which the output sequence is obtained for a given input sequence by solving an equation formed by pre-collected data. The condition under which the problem gives a solution is investigated and turns out to be L-delay invertibility of the plant and a certain degree of persist…
This paper addresses the output synchronization problem for heterogeneous nonlinear multi-agent systems with distributed event-based controllers. Employing the two-step synchronization process, we first outline the distributed event-triggered consensus controllers for linear reference models under a directed communication topology. It is further shown that the subsequent triggering instants are based on intermittent communication. Secondly, by using certain input-to-state stability (ISS) property, we design an event-triggered perturbed output regulation controller for each nonlinear multi-agen…
The fact that event-triggered control (ETC) often exhibits an improved performance-communication tradeoff over time-triggered control renders it especially useful for Networked Control Systems (NCSs). However, it has proven difficult to characterize the traffic produced by ETC a priori. Rollout ETC addresses this issue by using a triggering and control law that is implicitly defined by the solution to an optimal control problem (OCP), instead of an explicit one as in classical ETC. This allows to directly incorporate predefined constraints on the transmission traffic as well as on states and i…
We present a data-based approach to design event-triggered state-feedback controllers for unknown continuous-time linear systems affected by disturbances. By an event, we mean state measurements transmission from the sensors to the controller over a digital network. By exploiting a sufficiently rich finite set of noisy state measurements and inputs collected off-line, we first design a data-driven state-feedback controller to ensure an input-to-state stability property for the closed-loop system ignoring the network. We then take into account sampling induced by the network and we present robu…
Self-triggered control (STC) is a resource efficient approach to determine sampling instants for Networked Control Systems. At each sampling instant, an STC mechanism determines not only the control inputs but also the next sampling instant. In this article, an STC framework for perturbed nonlinear systems is proposed. In the framework, a dynamic variable is used in addition to current state information to determine the next sampling instant, rendering the STC mechanism dynamic. Using dynamic variables has proven to be powerful for increasing sampling intervals for the closely related concept …
This paper studies the design of feedback controllers to steer a switching linear time-invariant dynamical system towards the solution trajectory of a time-varying convex optimization problem. We propose two types of controllers: (i) a continuous controller inspired by the online gradient descent method, and (ii) a hybrid controller that can be interpreted as an online version of Nesterov's accelerated gradient method with restarts of the state variables. By design, the controllers continuously steer the system towards the time-varying optimizer without requiring knowledge of exogenous disturb…
Deep Reinforcement Learning Optimization for Uncertain Nonlinear Systems via Event-Triggered Robust Adaptive Dynamic Programming
Department of Computer Science, University College London（计算机科学系，伦敦大学学院）；Department of Electrical and Electronic Engineering, University of Manchester（电子与电气工程系，曼彻斯特大学）
This paper considers the control of uncertain systems that are operated under limited resource factors, such as battery life or hardware longevity. We consider here resource-aware self-triggered control techniques that schedule system operation non-uniformly in time in order to balance performance against resource consumption. When running in an uncertain environment, unknown disturbances may deteriorate system performance by acting adversarially against the planned event triggering schedule. In this work, we propose a resource-aware stochastic predictive control scheme to tackle this challeng…
Recent developments in cyber-physical systems and event-triggered control have led to an increased interest in the impact of sparse disturbances on dynamical processes. We study Linear Quadratic Regulator (LQR) control under sparse disturbances by analyzing three distinct policies: the blind online policy, the disturbance-aware policy, and the optimal offline policy. We derive the two-dimensional recurrence structure of the optimal disturbance-aware policy, under the assumption that the controller has information about future disturbance values with only a probabilistic model of their location…
In this work, we derive a region-based self-triggered control (STC) scheme for nonlinear systems with bounded disturbances and model uncertainties. The proposed STC scheme is able to guarantee different performance specifications (e.g. stability, boundedness, etc.), depending on the event-triggered control (ETC) triggering function that is chosen to be emulated. To deal with disturbances and uncertainties, we employ differential inclusions (DIs). By introducing ETC/STC notions in the context of DIs, we extend well-known results on ETC/STC to perturbed uncertain systems. Given these results, an…
General nonlinear continuous-time systems are considered for which its state is estimated via a packet-based communication network. We assume that the system has multiple sensor nodes, affected by measurement noise, which can transmit at discrete (non-equidistant) points in time. Moreover, each node can transmit asynchronously. For this setup, we develop a state estimation framework, where the transmission instances of the individual sensor nodes can be generated in either time-triggered or event-triggered fashions. In the latter case, we guarantee the absence of Zeno behavior by construction.…
This paper proposes an event-triggered sliding mode control (SMC) scheme combined with a backstepping algorithm for control of 2-DOF humanoid's lower-limb powered by Series elastic actuator (SEA). First, the modelling process for the lower-limb system is implemented by using the Euler-Lagrange theory. With the obtained dynamical equations of lower-limb, the model of the SEA is achieved in both mechanical and electrical perspectives. Then, the event-triggered SMC approach is utilized to ensure the system's stability and eliminate the effect of bounded external disturbance. Next, some assumption…
We study the platoon control of vehicles with third-order nonlinear dynamics under the constant spacing policy. We consider a vehicle model with parameter uncertainties and external disturbances and propose a distributed control law based on an event-triggered extended state observer (ESO). First, an event-triggered ESO is designed to estimate the unmodeled dynamics in the vehicle model. Then based on the estimate of the unmodeled dynamics, a distributed control law is designed by using a modified dynamic surface control method. The control law of each follower vehicle only uses the informatio…
This paper studies the formation stabilization problem of asynchronous nonlinear multi-agent systems (MAS) subject to parametric uncertainties, external disturbances and bounded time-varying communication delays. A self-triggered min-max distributed model predictive control (DMPC) approach is proposed to handle these practical issues. At triggering instants, each agent solves a local min-max optimization problem based on local system states and predicted system states of neighbors, determines its next triggering instant and broadcasts its predicted state trajectory to its neighbors. As a resul…
