Estimation of unmeasured variables is a crucial objective in a broad range of applications. However, the estimation process turns into a challenging problem when the underlying model is nonlinear and even more so when additionally it exhibits multiple time scales. The existing results on estimation for systems with two time scales apply to a limited class of nonlinear plants and observers. We focus on analyzing nonlinear observers designed for the slow state variables of nonlinear singularly perturbed systems. Moreover, we consider the presence of bounded measurement noise in the system. We generalize current results by considering broader classes of plants and estimators to cover reduced‐order, full‐order, and higher‐order observers. First, we show that the singularly perturbed system has bounded solutions under an appropriate set of assumptions on the corresponding boundary layer and reduced systems. We then exploit this property to prove that, under reasonable assumptions, the error dynamics of the observer designed for the reduced system are semiglobally input‐to‐state practically stable when the observer is implemented on the original plant. We also conclude ℒ2 stability results when the measurement noise belongs to ℒ2∩ℒ∞ . In the absence of measurement noise, we state results on semiglobal practical asymptotical stability for the error dynamics. We illustrate the generality of our main results through three classes of systems with corresponding observers and one numerical example.

We propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviors for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: One, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behavior. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented.

We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a network, and we provide sufficient conditions on the latter to preserve the stability property of the observer. In particular, we provide a bound on the maximum allowable transmission interval (MATI) that guarantees an input-to-state stability (ISS) property for the corresponding estimation error system. The stability analysis is trajectory-based, utilizes small-gain arguments, and exploits a persistently exciting property of the scheduling protocols. This property is key in our analysis and allows us to obtain significantly larger MATI bounds in comparison to the ones found in the literature. Our results hold for a general class of NCSs; however, we show that these results are also applicable to NCSs implemented over a specific physical network called WirelessHART (WH). The latter is mainly characterized by its multihop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We show that our results can be further improved by taking into account the intrinsic structure of the WH–NCS model. That is, we explicitly exploit the model structure in our analysis to obtain an even tighter MATI bound that guarantees the same ISS property for the estimation error system. Finally, to illustrate our results, we present analysis and numerical simulations for a class of Lipschitz nonlinear systems and high-gain observers.

Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.

The term stealthy has come to encompass a variety of techniques that attackers can employ to avoid being detected. In this manuscript, for a class of perturbed linear time-invariant systems, we propose two security metrics to quantify the potential impact that stealthy attacks could have on the system dynamics by tampering with sensor measurements. We provide analysis tools to quantify these metrics for given system dynamics, control, and system monitor. Then, we provide synthesis tools (in terms of semidefinite programs) to redesign controllers and monitors such that the impact of stealthy attacks is minimized and the required attack-free system performance is guaranteed.

Motivated by (approximate) dynamic programming and model predictive control problems, we analyse the stability of deterministic nonlinear discrete-time systems whose inputs minimize a discounted finite-horizon cost. We assume that the system satisfies stabilizability and detectability properties with respect to the stage cost. Then, a Lyapunov function for the closed-loop system is constructed and a uniform semiglobal stability property is ensured, where the adjustable parameters are both the discount factor and the horizon length, which corresponds to the number of iterations for dynamic programming algorithms like value iteration. Stronger stability properties such as global exponential stability are also provided by strengthening the initial assumptions. We give bounds on the discount factor and the horizon length under which stability holds and we provide conditions under which these are less conservative than the bounds of the literature for discounted infinite-horizon cost and undiscounted finite-horizon costs, respectively. In addition, we provide new relationships between the optimal value functions of the discounted, undiscounted, infinite-horizon and finite-horizon costs respectively, which are very different from those available in the approximate dynamic programming literature. These relationships rely on assumptions that are more likely to be satisfied in a control context. Finally, we investigate stability when only a near-optimal sequence of inputs for the discounted finite-horizon cost is available, covering approximate value iteration as a particular case.

For certain industrial control applications an explicit function capturing the non-trivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the human-learned cost function and an optimisation algorithm that can efficiently deal with a large number of variables, is used for optimising the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.

Constant-force contact-mode atomic force microscopy (AFM) relies on a feedback control system to regulate the tip–sample interaction during imaging. Due to limitations in actuators and control, the bandwidth of the regulation system is typically small. Therefore, the scan rate is usually limited in order to guarantee a desirable image quality for a constant-rate scan. By adapting the scan rate online, further performance improvement is possible, and the conditions to this improvement have been explored qualitatively in a previous study for a wide class of possible scan patterns. In this article, a quantitative assessment of the previously proposed adaptive scan scheme is investigated through experiments that explore the impact of various degrees of freedom in the algorithm. Further modifications to the existing scheme are proposed and shown to improve the closed-loop performance. The flexibility of the proposed approach is further demonstrated by applying the algorithm to tapping-mode AFM.

Periodic event-triggered control (PETC) is an appealing paradigm for the implementation of controllers on platforms with limited communication resources, a typical example being networked control systems. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario, where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the control inputs available locally, to decide whether a transmission is needed over the considered network. Following the emulation approach, we show how to design local triggering generators to ensure input-to-state stability and $\mathcal {L}_p$ stability for the overall system based on a continuous-time output-feedback controller that robustly stabilizes the network-free system. The method is applied to a class of Lipschitz nonlinear systems, for which we formulate the design conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.

Abstract Information about the system state is obtained through noisy sensor measurements. This data is coded and transmitted to a trusted user through an unsecured communication network. We aim at keeping the system state private; however, because the network is not secure, opponents might access sensor data, which can be used to estimate the state. To prevent this, before transmission, we randomize coded sensor data by passing it through a probabilistic mapping, and send the corrupted data to the trusted user. Making use of the data processing inequality, we cast the synthesis of the probabilistic mapping as a convex program where we minimize the mutual information (our privacy metric) between two estimators, one constructed using the randomized sensor data and the other using the actual undistorted sensor measurements, for a desired level of distortion–how different coded sensor measurements and distorted data are allowed to be.

This manuscript addresses the parameter and state estimation problem for continuous time nonlinear systems with unknown slowly time-varying parameters, which are assumed to belong to a known compact set. The problem is tackled by using the multi-observer approach under the supervisory framework, which generates parameter and state estimates by using a finite number of sample points of the parameter set, a bank of observers, a set of monitoring signals and a selection criterion. This note proposes a novel dynamic sampling policy for the multiobserver technique and studies its convergence properties. We prove that the parameter and state estimation errors are ultimately bounded where the ultimate bounds can be made arbitrarily small if the parameter varies sufficiently slowly, and the number of samples is sufficiently large.

Abstract A framework for tuning the parameters of model predictive controllers (MPCs) based on gradient-free optimisation (GFO) is proposed. Efficient calibration of MPCs is often a difficult task given the large number of tuning parameters and their non-intuitive correlation with the output response. We propose an efficient and systematic framework for the tuning of MPC parameters that can be implemented iteratively within the closed-loop setting. The performance of the proposed GFO-based algorithm is evaluated through its application to air-path control for diesel engines over simulations and experiments. We illustrate that the tuned parameters provide satisfactory tracking of reference trajectories over engine drive cycles with only a few iterations. Thereby, we extend existing MPC tuning approaches that calibrate parameters using step responses on the fuel rate and engine speed onto tuning over a full drive cycle response.

We study a class of distributed optimization problems of minimizing the sum of potentially non-differentiable convex objective functions (without requiring strong convexity). A novel approach to the analysis of asynchronous distributed optimization is developed. An iterative algorithm based on dual decomposition and block coordinate ascent is implemented in an edge based manner. We extend available results in the literature by allowing multiple and potentially overlapping blocks to be updated at the same time with non-uniform probabilities assigned to different blocks. Sublinear convergence with probability one is proved for the algorithm under the aforementioned weak assumptions. A numerical example is provided to illustrate the effectiveness of the algorithm.

Value iteration is a method to generate optimal control inputs for generic nonlinear systems and cost functions. Its implementation typically leads to approximation errors, which may have a major impact on the closed-loop system performance. We talk in this case of approximate value iteration (AVI). In this paper, we investigate the stability of systems for which the inputs are obtained by AVI. We consider deterministic discrete-time nonlinear plants and a class of general, possibly discounted, costs. We model the closed-loop system as a family of systems parameterized by tunable parameters, which are used for the approximation of the value function at different iterations, the discount factor and the iteration step at which we stop running the algorithm. It is shown, under natural stabilizability and detectability properties as well as mild conditions on the approximation errors, that the family of closed-loop systems exhibit local practical stability properties. The analysis is based on the construction of a Lyapunov function given by the sum of the approximate value function and the Lyapunov-like function that characterizes the detectability of the system. By strengthening our conditions, asymptotic and exponential stability properties are guaranteed.

We propose a novel triggering policy to implement state-feedback controllers for nonlinear systems via packet-based communication networks. The idea is to generate transmissions between the plant and the controller only when a state-dependent rule has been satisfied for a given amount of time. We refer to this new paradigm as event-holding control, in which a clock variable is thus only running when a state-dependent criterion is verified. This is different from time-regularized event-triggered control, where the clock variable keeps running after each transmission instant until it is reset to zero at the moment a state-based condition is verified. We approach the problem of designing an event-holding controller via emulation. We first synthesize a state-feedback law, which stabilizes the closed-loop system in the absence of the communication network. We then design the event-holding triggering mechanism under a set of general assumptions. The results are applied to two case studies consisting of linear systems and a class of nonlinear systems controlled by backstepping. We also provide a numerical backstepping control example, which demonstrates that the event-holding behaviour can reduce the number of transmissions.