This article presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms prediction horizon and magnitude derivatives system states. Using higher order general need not be known, we construct Koopman-operator-based linear representation utilize Taylor series accuracy analysis to derive an bound. The resulting formula is used choose basis functions obtain Koopman using closed-form expression can computed real time. inverted...

This paper presents a data-driven methodology for linear embedding of nonlinear systems.Utilizing structural knowledge general dynamics, the authors exploit Koopman operator to develop systematic, approach constructing representation in terms higher order derivatives underlying dynamics.With representation, system is then controlled with an LQR feedback policy, gains which need be calculated only once.As result, enables fast control synthesis.We demonstrate efficacy simulations and...

In this article, we demonstrate the benefits of imposing stability on data-driven Koopman operators. The identification stable operators (DISKO) is implemented using an algorithm [1] that computes nearest <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stable</i> matrix solution to a least-squares reconstruction error. As first result, derive formula describes prediction error representations for arbitrary number time steps, and which shows...

Interest in soft robotics has increased recent years due to their potential a myriad of applications. A wide variety robots emerged, including bio-inspired robotic swimmers such as jellyfish, rays, and fish. However, the highly nonlinear fluid-structure interactions pose considerable challenges analysis, modeling, feedback control these swimmers. In particular, developing models that are high fidelity but also amenable for remains an open problem. this work, we propose data-driven approach...

Model predictive control (MPC) is a powerful feedback technique that often used in data-driven robotics. The performance of MPC depends on the accuracy model, which requires careful tuning. Furthermore, specifying task with an objective function and synthesizing policy are not straightforward typically lead to suboptimal solutions driven by trial error. To address these challenges, we present method jointly optimize system identification, specification, synthesis unknown dynamical systems....

This paper derives nonlinear feedback control synthesis for general affine systems using second-order actions, the needle variations of optimal control, as basis choosing each response to current state. A second result this is that method provably exploits controllability a system by virtue an explicit dependence variation on Lie bracket between vector fields. As result, decision necessarily decreases objective when nonlinearly controllable first-order brackets. Simulation results...

This paper uses Sequential Action Control (SAC), a model-based method for control of non-linear systems, fast, optimal trajectory-tracking tasks in the presence fluid drift. Through benchmark example kinematic car, it is shown that SAC outperforms traditional offline projection - based optimization technique terms effort and objective cost. Motivated by recent work on effort-efficient, sight-independent weakly electric fish, this papers also shows successfully provides control-optimal...

This paper presents robust Koopman model predictive control (RK-MPC), a framework that leverages the training errors of data-driven models to improve constraint satisfaction. Koopman-based has enabled fast nonlinear feedback using linear tools, but existing approaches ignore modeling error during control, which can lead violations. Our approach assumes unknown dynamics are Lipschitz-continuous and uses approximate Lipschitz constant for state- control-dependent error. We then use bound...

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as powerful modeling learning-based control method enabling significant advancements across various domains robotics. Due to its ability represent nonlinear linear operator, fresh lens through which understand tackle the complex robotic systems. Moreover, it enables incremental updates is computationally inexpensive making particularly appealing for real-time applications online active learning. This review...

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose novel algorithm for learning LDSs. Using recent characterization matrices, we present an optimization method ensures at every step iteratively improves using gradient directions derived in this paper. When applied to LDSs with inputs, our approach---in contrast current methods LDSs---updates state control...

This paper demonstrates the benefits of imposing stability on data-driven Koopman operators. The identification stable operators (DISKO) is implemented using an algorithm \cite{mamakoukas_stableLDS2020} that computes nearest \textit{stable} matrix solution to a least-squares reconstruction error. As first result, we derive formula describes prediction error representations for arbitrary number time steps, and which shows constraints can improve predictive accuracy over long horizons. second...

In recent years, gliding robotic fish have emerged as promising mobile platforms for underwater sensing and monitoring due to their notable energy efficiency maneuverability. For of aquatic environments, it is important use efficient sampling strategies that incorporate previously observed data in deciding where sample next so the gained information maximized. this paper, we present an adaptive strategy mapping a scalar field environment using fish. An ergodic exploration framework employed...

This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from first-and mode insertion gradients objective and are proven to exhibit superlinear near equilibrium. Compared first-order variations, proposed synthesis scheme exhibits superior at smaller computational cost than alternative feedback controllers. Simulation results on differential drive model...

Abstract This paper presents an adaptive, needle variation-based feedback scheme for controlling affine nonlinear systems with unknown parameters that appear linearly in the dynamics. The proposed approach combines online parameter identifier a second-order sequential action controller has shown great promise nonlinear, underactuated, and high-dimensional constrained systems. Simulation results on dynamics of underwater glider robotic fish show advantages introducing estimation to when model...

This paper derives nonlinear feedback control synthesis for general affine systems using second-order actions-the needle variations of optimal control-as the basis choosing each response to current state.A second result is that method provably exploits controllability a system by virtue an explicit dependence variation on Lie bracket between vector fields.As result, decision necessarily decreases objective when nonlinearly controllable first-order brackets.Simulation results differential...

This paper derives nonlinear feedback control synthesis for general affine systems using second-order actions---the needle variations of optimal control---as the basis choosing each response to current state. A second result is that method provably exploits controllability a system by virtue an explicit dependence variation on Lie bracket between vector fields. As result, decision necessarily decreases objective when nonlinearly controllable first-order brackets. Simulation results...

This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms prediction horizon and magnitude derivatives system states. Using higher-order general need not be known, we construct Koopman operator-based linear representation utilize Taylor series accuracy analysis to derive an bound. The resulting formula is used choose order basis functions obtain using closed-form expression can computed real time. inverted...