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.
In this paper, we establish a unified framework for subspace identification (SID) of linear parameter-varying (LPV) systems to estimate LPV state-space (SS) models in innovation form. This framework enables us to derive novel LPV SID schemes that are extensions of existing linear time-invariant (LTI) methods. More specifically, we derive the open-loop, closed-loop, and predictor-based data-equations, an input-output surrogate form of the SS representation, by systematically establishing an LPV subspace identification theory. We show the additional challenges of the LPV setting compared to the …
In this paper, we develop a system identification algorithm to identify a model for unknown linear quantum systems driven by time-varying coherent states, based on empirical single-shot continuous homodyne measurement data of the system's output. The proposed algorithm identifies a model that satisfies the physical realizability conditions for linear quantum systems, challenging constraints not encountered in classical (non-quantum) linear system identification. Numerical examples on a multiple-input multiple-output optical cavity model are presented to illustrate an application of the identif…
Time-varying hierarchical multi-agent systems are common in many applications. A well-known solution to control these systems is to use state feedback controllers that depend on the adjacency matrix to reach consensus. This solution has been applied so far to multi-agent systems with fixed or time-varying communication topologies. In this paper, we consider single-integrator multi-agent systems where only a subset of the agents are active at any given time and the set of active agents is time-varying. This type of multi-agent system is relevant in applications such as modular multilevel conver…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be modelled as systems experiencing limit cycle behavior. The goal of this work is to identify from data, the local dynamics around the limit cycle using linear periodically parameter-varying models. Using a coordinate transformation onto transversal surfaces, the dynamics are decomposed into two parts: one along the limit cycle, and one on the transversal surf…
This paper describes the LPVcore software package for MATLAB developed to model, simulate, estimate and control systems via linear parameter-varying (LPV) input-output (IO), state-space (SS) and linear fractional (LFR) representations. In the LPVcore toolbox, basis affine parameter-varying matrix functions are implemented to enable users to represent LPV systems in a global setting, i.e., for time-varying scheduling trajectories. This is a key difference compared to other software suites that use a grid or only LFR-based representations. The paper contains an overview of functions in the toolb…
System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying (LTV) systems. To tackle this challenge, we develop an episodic block model for the LTV system where the model parameters remain constant within each block but change from block to block. Based on the observation that the model parameters across different blocks are related, we treat each episodic block as a learning task and then run meta-learning over many…
Hybrid electric vehicles (HEVs) have an over-actuated system by including two power sources, a battery pack and an internal combustion engine. This feature of HEV is exploited in this paper to simultaneously achieve accurate identification of battery parameters/states. By actively injecting current signals, state of charge, state of health, and other battery parameters can be estimated in a specific sequence to improve the identification performance when compared to the case where all parameters and states are estimated concurrently using the baseline current signals. A dynamic programming str…
Many active noise and vibration control systems require models of the control paths. When the controlled system changes slightly over time, adaptive digital filters for the identification of the models are useful. This paper aims at the investigation of a special class of adaptive digital filters: Orthonormal filter banks possess the robust and simple adaptation of the widely applied Finite Impulse Response (FIR) filters, but at a lower model order, which is important when considering implementation on embedded systems. However, the filter banks require prior knowledge about the resonance freq…
This work proposes an online adaptive identification method for multi-input multi-output (MIMO) switched affine systems with guaranteed parameter convergence. A family of online parameter estimators is used that is equipped with a dual-layer low pass filter architecture to facilitate parameter learning and identification of each subsystem. The filters capture information about the unknown parameters in the form of a prediction error which is used in the parameter estimation algorithm. A salient feature of the proposed method that distinguishes it from most previous results is the use of a memo…
Paul G. Allen School of Computer Science & Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound quantifying the estimation rate our algorithm attains and prove matching upper and lower bounds which guarantee its asymptotic optimality, up to constants. In addition, we show that this optimal rate is unattainable when using Gaussian noise to excite the system, even with optimally tuned covariance, and analyze several examples where our algorithm provably impr…
Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods
Department of Automation；Systems Engineering, Federal University of Santa Catarina, Florianópolis, 88040-900, Santa Catarina, Brazil；Harold Vance Department of Petroleum Engineering, Texas A\&M University, College Station, 77843-3116, Texas, USA
Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
IMT School for Advanced Studies Lucca（IMT卢卡高等研究院）；Eindhoven University of Technology（埃因霍温理工大学）；HUN-REN Institute for Computer Science and Control（匈牙利科学院计算机科学与控制研究所（HUN-REN））
Norwegian University of Science and Technology（挪威科技大学）；SINTEF Digital（SINTEF数字研究所）
The exploding research interest for neural networks in modeling nonlinear dynamical systems is largely explained by the networks' capacity to model complex input-output relations directly from data. However, they typically need vast training data before they can be put to any good use. The data generation process for dynamical systems can be an expensive endeavor both in terms of time and resources. Active learning addresses this shortcoming by acquiring the most informative data, thereby reducing the need to collect enormous datasets. What makes the current work unique is integrating the deep…
Active Sensing and Deferred-Decision Trajectory Optimization for Robust Target Identification
Department of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程系）；Department of Electrical Engineering, University of Notre Dame（诺丁汉大学电气工程系）
With the commitment to climate, globally many countries started reducing brownfield energy production and strongly opting towards green energy resources. However, the optimal allocation of distributed energy resources (DERs) in electrical distribution systems still pertains as a challenging issue to attain the maximum benefits. It happens due to the systems complex behaviour and inappropriate integration of DERs that adversely affects the distribution grid. In this work, we propose a methodology for the optimal allocation of DERs with vulnerable node identification in active electrical distrib…
Online sparse Bayesian identification of nonlinear time-varying systems
College of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan, 030024, China（电气与电力工程学院，太原理工大学，太原，030024，中国）；Department of Automation, Taiyuan Institute of Technology, Taiyuan, 030024, China（自动化系，太原理工大学，太原，030024，中国）
