State Estimation of Continuous-time Dynamical Systems with Uncertain Inputs with Bounded Variation: Entropy, Bit Rates, and Relation with Switched Systems
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$ε$}-estimation entropy of the system and show that it lower bounds the bit rate needed for state estimation. {$ε$}-estimation entropy represents the exponential rate of the increase of the minimal number of functions that are adequate for {$ε$}- approximating any trajectory of the system. We show that alternative entropy definitions using spanning or separating trajectories bound ours from both sides. On the other hand, we show that other commonly used definitions of entropy, for example the ones in [1], diverge to infinity. Thus, they are potentially not suitable for systems with uncertain inputs. We derive an upper bound on {$ε$}-estimation entropy and estimation bit rates, and evaluate it for two examples. We present a state estimation algorithm that constructs a function that approximates a given trajectory up to an {$ε$} error, given time-sampled and quantized measurements of state and input. We investigate the relation between {$ε$}-estimation entropy and a previous notion for switched nonlinear systems and derive a new upper bound for the latter, showing the generality of our results on systems with uncertain inputs.
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special consideration for handling switching uncertainties. The resulting infinite-dimensional linear programs can be solved approximately with Linear Matrix Inequalities arising from the moment-SOS hierarch…
Stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays
This paper considers a scenario of pursuing a moving target that may switch behaviors due to external factors in a dynamic environment by motion estimation using visual sensors. First, we present an improved Visual Motion Observer with switched Gaussian Process models for an extended class of target motion profiles. We then propose a pursuit control law with an online method to estimate the switching behavior of the target by the GP model uncertainty. Next, we prove ultimate boundedness of the control and estimation errors for the switch in target behavior with high probability. Finally, a Dig…
Cooperative Switched Formation Control of Autonomous Vehicles: An Event-triggered Approach to Input Saturation and Time-delay Challenges
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；KTH Royal Institute of Technology（皇家理工学院）
Cooperative Target Capture in 3D Engagements over Switched Dynamic Graphs
Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（智能系统指导、自主、学习与控制实验室，航空航天工程与工程力学系，辛辛那提大学）；Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay（智能系统与控制实验室，航空航天工程系，印度班加罗尔理工学院）
The deployment of autonomous systems that operate in unstructured environments necessitates algorithms to verify their safety. This can be challenging due to, e.g., black-box components in the control software, or undermodelled dynamics that prevent model-based verification. We present a novel verification framework for an unknown dynamical system from a given set of noisy observations of the dynamics. Using Gaussian processes trained on this data set, the framework abstracts the system as an uncertain Markov process with discrete states defined over the safe set. The transition bounds of the …
