We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals. Leveraging affine abstraction methods and the existence of nonlinear decomposition functions, as well as applying our previously developed data-driven function over-approximation/abstraction approach to over-estimate the unknown dynamic model, our proposed observer recursively computes the maximal and minimal elements of the estimate intervals that are proven to contain the true augmented states. Then, using observed output/measurement signals, the observer iteratively shrinks the intervals by eliminating estimates that are not compatible with the measurements. Finally, given new interval estimates, the observer updates the over-approximation of the unknown model dynamics. Moreover, we provide sufficient conditions for uniform boundedness of the sequence of estimate interval widths, i.e., stability of the designed observer, in the form of tractable (mixed-)integer programs with finitely countable feasible sets.
Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer …
A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is proposed. The presented novel solution estimates the vehicle's pose (i.e. attitude and position) with respect to landmarks simultaneously positioning the reference features in the global frame. The proposed estimator on manifold is characterized by predefined measures of transient and steady-state performance. Dynamically reducing boundaries guide the error function of the system to reduce asymptotically to the origin from its starting posit…
This paper considers the problem of designing interval observers for hidden mode switched nonlinear systems with bounded noise signals that are compromised by false data injection and switching attacks. The proposed observer consists of three components: i) a bank of mode-matched observers, which simultaneously estimates the corresponding mode-matched continuous states and discrete states (modes), as well as learns a model of the unknown attack policy, ii) a mode observer that eliminates the incompatible modes based on a residual-based set-membership criterion, and iii) a global fusion observe…
A simultaneous mode, input and state set-valued observer is proposed for hidden mode switched linear systems with bounded-norm noise and unknown input signals. The observer consists of two constituents: (i) a bank of mode-matched observers and (ii) a mode estimator. Each mode-matched observer recursively outputs the mode-matched sets of compatible states and unknown inputs, while the mode estimator eliminates incompatible modes, using a residual-based criterion. Then, the estimated sets of states and unknown inputs are the union of the mode-matched estimates over all compatible modes. Moreover…
A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the true state and inputs. The proposed observer can be designed using semidefinite programming with LMI constraints and is optimal in the minimum \mathcal{H}_{\infty}-norm sense. We show that the strong detectability of each constituent linear time-invariant system is a necessary condition for the existence of such an observer, as well as the boundedness of set-…
A simultaneous input and state interval observer is presented for Lipschitz continuous nonlinear systems with unknown inputs and bounded noise signals for the case when the direct feedthrough matrix has full column rank. The observer leverages the existence of bounding decomposition functions for mixed monotone mappings to recursively compute the maximal and minimal elements of the estimate intervals that are compatible with output/measurement signals, and are proven to contain the true state and unknown input. Furthermore, we derive a Lipschitz-like property for decomposition functions, which…
We address the problem of designing simultaneous input and state interval observers for Lipschitz continuous nonlinear systems with rank-deficient feedthrough, unknown inputs and bounded noise signals. Benefiting from the existence of nonlinear decomposition functions and affine abstractions, our proposed observer recursively computes the maximal and minimal elements of the estimate intervals that are proven to contain the true states and unknown inputs. Moreover, we provide necessary and sufficient conditions for the existence and sufficient conditions for the stability (i.e., uniform bounded…
In this paper, we study the problem of designing a simultaneous mode, input, and state set-valued observer for a class of hidden mode switched nonlinear systems with bounded-norm noise and unknown input signals, where the hidden mode and unknown inputs can represent fault or attack models and exogenous fault/disturbance or adversarial signals, respectively. The proposed multiple-model design has three constituents: (i) a bank of mode-matched set-valued observers, (ii) a mode observer, and (iii) a global fusion observer. The mode-matched observers recursively find the sets of compatible states …
In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes of nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of Linear Matrix Inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for ($\mathcal{M},γ$)- Quadratically Constrained (($\mathcal{M},γ$)-QC) systems, which includes several classes of nonlinea…
The process of simultaneously mapping the environment in three dimensional (3D) space and localizing a moving vehicle's pose (orientation and position) is termed Simultaneous Localization and Mapping (SLAM). SLAM is a core task in robotics applications. In the SLAM problem, each of the vehicle's pose and the environment are assumed to be completely unknown. This paper takes the conventional SLAM design as a basis and proposes a novel approach that ensures fast adaptation of the nonlinear observer for SLAM. Due to the fact that the true SLAM problem is nonlinear and is modeled on the Lie group …
University of Padova（帕多瓦大学）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
In this paper, we propose a Model-Based Reinforcement Learning (MBRL) algorithm for Partially Measurable Systems (PMS), i.e., systems where the state can not be directly measured, but must be estimated through proper state observers. The proposed algorithm, named Monte Carlo Probabilistic Inference for Learning COntrol for Partially Measurable Systems (MC-PILCO4PMS), relies on Gaussian Processes (GPs) to model the system dynamics, and on a Monte Carlo approach to update the policy parameters. W.r.t. previous GP-based MBRL algorithms, MC-PILCO4PMS models explicitly the presence of state observe…
Navigation solutions suitable for cases when both autonomous robot's pose (\textit{i.e}., attitude and position) and its environment are unknown are in great demand. Simultaneous Localization and Mapping (SLAM) fulfills this need by concurrently mapping the environment and observing robot's pose with respect to the map. This work proposes a nonlinear observer for SLAM posed on the manifold of the Lie group of $\mathbb{SLAM}_{n}\left(3\right)$, characterized by systematic convergence, and designed to mimic the nonlinear motion dynamics of the true SLAM problem. The system error is constrained t…
POMDPs are useful models for systems where the true underlying state is not known completely to an outside observer; the outside observer incompletely knows the true state of the system, and observes a noisy version of the true system state. When the number of system states is large in a POMDP that often necessitates the use of approximation methods to obtain near optimal solutions for control. This survey is centered around the origins, theory, and approximations of finite-state POMDPs. In order to understand POMDPs, it is required to have an understanding of finite-state Markov Decision Proc…
This paper proposes an observer-based framework for solving Partially Observable Markov Decision Processes (POMDPs) when an accurate model is not available. We first propose to use a Moving Horizon Estimation-Model Predictive Control (MHE-MPC) scheme in order to provide a policy for the POMDP problem, where the full state of the real process is not measured and necessarily known. We propose to parameterize both MPC and MHE formulations, where certain adjustable parameters are regarded for tuning the policy. In this paper, for the sake of tackling the unmodeled and partially observable dynamics…
We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design…
A robust nonlinear stochastic observer for simultaneous localization and mapping (SLAM) is proposed using the available uncertain measurements of angular velocity, translational velocity, and features. The proposed observer is posed on the Lie Group of $\mathbb{SLAM}_{n}\left(3\right)$ to mimic the true stochastic SLAM dynamics. The proposed approach considers the velocity measurements to be attached with an unknown bias and an unknown Gaussian noise. The proposed SLAM observer ensures that the closed loop error signals are semi-globally uniformly ultimately bounded. Simulation results demonst…
In this paper, we simultaneously determine the optimal sensor precision and the observer gain, which achieves the specified accuracy in the state estimates. Along with the unknown observer gain, the formulation parameterizes the scaling of the exogenous inputs that correspond to the sensor noise. Reciprocal of this scaling is defined as the sensor precision, and sparseness is achieved by minimizing the $l_1$ norm of the precision vector. The optimization is performed with constraints guaranteeing specified accuracy in state estimates, which are defined in terms of $\mathcal{H}_2$ or $\mathcal{…
In this note, we develop an adaptive observer for a class of nonlinear systems with switched unknown parameters to estimate the states and parameters simultaneously. The main challenge lies in how to eliminate the disturbance effect of zero-input responses caused by the switching on the parameter estimation. These responses depend on the unknown states at switching instants (SASI) and constitute an additive disturbance to the parameter estimation, which obstructs parameter convergence to zero. Our solution is to treat the zero-input responses as excitations instead of disturbances. This is rea…
Phasor measurement units ({PMUs}) have become instrumental in modern power systems for enabling real-time, wide-area monitoring and control. Accordingly, many studies have investigated efficient and robust dynamic state estimation (DSE) methods in order to accurately compute the dynamic states of generation units. Nonetheless, most of them forego the dynamic-algebraic nature of power networks and only consider their nonlinear dynamic representations. Motivated by the lack of DSE methods based on power network's differential-algebraic equations (DAEs), this paper develops a novel observer-based…
Australian Centre for Field Robotics & Sydney Institute for Robotics and Intelligent Systems, The University of Sydney（悉尼大学澳大利亚野外机器人中心与悉尼机器人与智能系统研究所）；DJI Innovation Inc.（大疆创新科技有限公司）
In this paper we propose a novel observer to solve the problem of visual simultaneous localization and mapping (SLAM), only using the information from a single monocular camera and an inertial measurement unit (IMU). The system state evolves on the manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully in order to generate an invariant foliation, such that the problem is reformulated into online \emph{constant parameter} identification. Then, following the recently introduced parameter estimation-based observer (PEBO) and the dynamic regressor extension and mix…
Western University（西安大略大学）；University of Quebec in Outaouais（魁北克大学乌塔韦校区）；Lakehead University（湖首大学）
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and…
This is the last part of four series papers, aiming at stabilization for signal-input-signaloutput (SISO) linear finite-dimensional systems corrupted by general input disturbances. A new observer, referred to as Extended Dynamics Observer (EDO), is proposed to estimate both the state and disturbance simultaneously. The working mechanism of EDO consists of two parts: The disturbance with known dynamics is canceled completely by its dynamics and the disturbance with unknown dynamics is absorbed by high-gain. It is found that the high-gain is always working as long as the control plant with unkno…
Thompson Rivers University（汤普森河大学）；The Hong Kong Polytechnic University（香港理工大学）
Simultaneous Localization and Mapping (SLAM) is a process of concurrent estimation of the vehicle's pose and feature locations with respect to a frame of reference. This paper proposes a computationally cheap geometric nonlinear SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the true SLAM problem posed on the matrix Lie group of $\mathbb{SLAM}_{n}\left(3\right)$. The nonlinear filter on manifold is proposed in continuous form and it utilizes available measurements obtained from group velocity vectors, feature measurements and an inertial measurement unit (IMU). The …
This paper considers the simultaneous state and unknown input estimation for continuous-discrete stochastic systems. Two types of approaches (with and without modeling of unknown inputs) which can address this issue are investigated. A novel continuous recursive four-step Kalman filter is proposed and its asymptotic stability condition is established. A novel one-step unknown input Kalman filter is proposed and has guaranteed stability when the number of unknown inputs is equal to that of the measurements. The design of unknown input Kalman filters and observers is unified. Furthermore, an ada…
Western University（韦仕敦大学）；Lakehead University（湖首大学）
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular velocity and linear acceleration measurements as well as intermittent landmark position measurements. The first type relies on a fixed-gain design approach based on an infinite-dimensional optimization, while the second one relies on a variable-gain design approach based on a continuous-discrete Riccati equation. For each case, we provide two different observers…
Cooperative Integrated Estimation-Guidance for Simultaneous Interception of Moving Targets
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，印度理工学院班加罗尔）；Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（智能系统引导、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）
This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, wher…
In this note, the problem of simultaneous leader-following consensus and parameter estimation is studied for a class of multi-agent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies and phases. A distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adap…
