Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm

A supervisory observer is a multiple-model architecture, which estimates the parameters and the states of nonlinear systems. It consists of a bank of state observers, where each observer is designed for some nominal parameter values sampled in a known parameter set. A selection criterion is used to select a single observer at each time instant, which provides its state estimate and parameter value. The sampling of the parameter set plays a crucial role in this approach. Existing works require a sufficiently large number of parameter samples, but no explicit lower bound on this number is provided. The aim of this work is to overcome this limitation by sampling the parameter set automatically using an iterative global optimisation method, called DIviding RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np parameter samples where np is the dimension of the parameter set. Then, the algorithm iteratively adds samples to improve its estimation accuracy. Convergence guarantees are provided under the same assumptions as in previous works, which include a persistency of excitation condition. The efficacy of the supervisory observer with the DIRECT sampling policy is illustrated on a model of neural populations

Adaptive voltage regulation of an inverter-based power distribution network with a class of droop controllers

The voltage received by each customer connected to a power distribution line with local controllers (inverters) is regulated to be within a desired margin through a class of slope-restricted controllers, known conventionally as \emph{droop} controllers. We adapt the design of the droop controllers according to the known bounds of the net power consumption of each customer in each observation time window. A sufficient condition for voltage regulation is provided for each time window, which guides the design of the droop controllers, depending on the properties of the distribution line (line impedances) and the upper bound of all the customers' power consumption during each time window. The resulting adaptive scheme is verified on a benchmark model of a European low-voltage network by the CIGRE task force.Comment: This work has been accepted to IFAC World Congress 2020 for publication under a Creative Commons Licence CC-BY-NC-N

Reachable set-based dynamic quantization for the remote state estimation of linear systems

We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission instant, with an approximated reachable set of the linear system. We propose a set-based method using zonotopes and compare it to a norm-based method in dynamically updating the quantization region. For both methods, we guarantee that the quantization error is bounded and consequently, the remote state reconstruction error is also bounded. To the best of our knowledge, the set-based method using zonotopes has no precedent in the literature and admits a larger class of linear systems and communication channels, where the set-based method allows for a longer inter-transmission time and lower bit rate. Finally, we corroborate our theoretical guarantees with a numerical example.Comment: This manuscript was accepted for publication at the 62nd IEEE Conference on Decision and Control (CDC), 202

Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming

We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of the control system, when starting from a given initial set, always remain in a prescribed safe set. We consider polynomial systems with semi-algebraic safe sets. Using the S-procedure for polynomial functions, safety conditions can be formulated as a Sum-Of-Squares (SOS) programme, which can be solved efficiently. When safety cannot be guaranteed, we provide tools via SOS to synthesize polynomial controllers that enforce safety of the closed loop system. The theoretical results are illustrated through numerical simulations

Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming

We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of the control system, when starting from a given initial set, always remain in a prescribed safe set. We consider polynomial systems with semi-algebraic safe sets. Using the S-procedure for polynomial functions, safety conditions can be formulated as a Sum-Of-Squares (SOS) programme, which can be solved efficiently. When safety cannot be guaranteed, we provide tools via SOS to synthesize polynomial controllers that enforce safety of the closed loop system. The theoretical results are illustrated through numerical simulations

A secure state estimation algorithm for nonlinear systems under sensor attacks

The state estimation of continuous-time nonlinear systems in which a subset of sensor outputs can be maliciously controlled through injecting a potentially unbounded additive signal is considered in this paper. Analogous to our earlier work for continuous-time linear systems in \cite{chong2015observability}, we term the convergence of the estimates to the true states in the presence of sensor attacks as `observability under $M$ attacks', where $M$ refers to the number of sensors which the attacker has access to. Unlike the linear case, we only provide a sufficient condition such that a nonlinear system is observable under $M$ attacks. The condition requires the existence of asymptotic observers which are robust with respect to the attack signals in an input-to-state stable sense. We show that an algorithm to choose a compatible state estimate from the state estimates generated by the bank of observers achieves asymptotic state reconstruction. We also provide a constructive method for a class of nonlinear systems to design state observers which have the desirable robustness property. The relevance of this study is illustrated on monitoring the safe operation of a power distribution network.Comment: This paper has been accepted for publication at the 59th IEEE Conference on Decision and Control, 202

Safety monitoring under stealthy sensor injection attacks using reachable sets

Stealthy sensor injection attacks are serious threats for industrial plants as they can compromise the plant's integrity without being detected by traditional fault detectors. In this manuscript, we study the possibility of revealing the presence of such attacks by monitoring only the control input. This approach consists in computing an ellipsoidal bound of the input reachable set. When the control input does not belong to this set, this means that a stealthy sensor injection attack is driving the plant to critical states. The problem of finding this ellipsoidal bound is posed as a convex optimization problem (convex cost with Linear Matrix Inequalities constraints). Our monitoring approach is tested in simulation

Secure Set-Based State Estimation for Linear Systems under Adversarial Attacks on Sensors

When a strategic adversary can attack multiple sensors of a system and freely choose a different set of sensors at different times, how can we ensure that the state estimate remains uncorrupted by the attacker? The existing literature addressing this problem mandates that the adversary can only corrupt less than half of the total number of sensors. This limitation is fundamental to all point-based secure state estimators because of their dependence on algorithms that rely on majority voting among sensors. However, in reality, an adversary with ample resources may not be limited to attacking less than half of the total number of sensors. This paper avoids the above-mentioned fundamental limitation by proposing a set-based approach that allows attacks on all but one sensor at any given time. We guarantee that the true state is always contained in the estimated set, which is represented by a collection of constrained zonotopes, provided that the system is bounded-input-bounded-state stable and redundantly observable via every combination of sensor subsets with size equal to the number of uncompromised sensors. Additionally, we show that the estimated set is secure and stable irrespective of the attack signals if the process and measurement noises are bounded. To detect the set of attacked sensors at each time, we propose a simple attack detection technique. However, we acknowledge that intelligently designed stealthy attacks may not be detected and, in the worst-case scenario, could even result in exponential growth in the algorithm's complexity. We alleviate this shortcoming by presenting a range of strategies that offer different levels of trade-offs between estimation performance and complexity

Hyperthermic laser ablation of recurrent glioblastoma leads to temporary disruption of the peritumoral blood brain barrier

BACKGROUND:Poor central nervous system penetration of cytotoxic drugs due to the blood brain barrier (BBB) is a major limiting factor in the treatment of brain tumors. Most recurrent glioblastomas (GBM) occur within the peritumoral region. In this study, we describe a hyperthemic method to induce temporary disruption of the peritumoral BBB that can potentially be used to enhance drug delivery. METHODS:Twenty patients with probable recurrent GBM were enrolled in this study. Fourteen patients were evaluable. MRI-guided laser interstitial thermal therapy was applied to achieve both tumor cytoreduction and disruption of the peritumoral BBB. To determine the degree and timing of peritumoral BBB disruption, dynamic contrast-enhancement brain MRI was used to calculate the vascular transfer constant (Ktrans) in the peritumoral region as direct measures of BBB permeability before and after laser ablation. Serum levels of brain-specific enolase, also known as neuron-specific enolase, were also measured and used as an independent quantification of BBB disruption. RESULTS:In all 14 evaluable patients, Ktrans levels peaked immediately post laser ablation, followed by a gradual decline over the following 4 weeks. Serum BSE concentrations increased shortly after laser ablation and peaked in 1-3 weeks before decreasing to baseline by 6 weeks. CONCLUSIONS:The data from our pilot research support that disruption of the peritumoral BBB was induced by hyperthemia with the peak of high permeability occurring within 1-2 weeks after laser ablation and resolving by 4-6 weeks. This provides a therapeutic window of opportunity during which delivery of BBB-impermeant therapeutic agents may be enhanced. TRIAL REGISTRATION:ClinicalTrials.gov NCT01851733