اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEstimating States for Nonlinear Systems Using the Particle Filter
117
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting with highly uncertain nonlinear dynamic systems. In this study, a nonlinear estimator is developed by adopting a particle filter algorithm that takes advantage of measured signals. This approach is shown to significantly improve the ability to estimate states. To illustrate this approach, a model for a nonlinear device coupled with a hydraulic actuator plays the role of an actual plant and a nonlinear algebraic function is considered as an approximation of the nonlinear device, thus generating non-parametric and parametric uncertainties. Then we use displacement and force signals to improve the distribution of the states by resampling the set of particles. Finally, all of the states are estimated from these posterior density functions. A set of simulations considering three different noise levels demonstrates that the performance of the particle filter approach is superior to the Kalman filter, yielding substantially better performance when estimating nonlinear physical systems in the presence of modeling uncertainties.
قيم البحث
اقرأ أيضاً
In this paper, we introduce an angle notion, called the singular angle, for stable nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $mathcal{L}_2$-signals, describes an upper bound for
the rotating effect from the system input to output signals. It is, thus, different from the recently appeared nonlinear system phase which adopts the complexification of real-valued signals using the Hilbert transform. It can quantify the passivity and serve as an angular counterpart to the system $mathcal{L}_2$-gain. It also provides an alternative to the nonlinear system phase. A nonlinear small angle theorem, which involves a comparison of the loop system angle with $pi$, is established for feedback stability analysis. When dealing with multi-input multi-output linear time-invariant (LTI) systems, we further come up with the frequency-wise and $mathcal{H}_infty$ singular angle notions based on the matrix singular angle, and develop corresponding LTI small angle theorems.
This paper focuses on developing a new paradigm motivated by investigating the consensus problem of networked Lagrangian systems with time-varying delay and switching topologies. We present adaptive controllers with piecewise continuous or arbitrary
times differentiable control torques for realizing consensus of Lagrangian systems, extending the results in the literature. This specific study motivates the formulation of a new paradigm referred to as forwardstepping, which is shown to be a systematic tool for solving various nonlinear control problems. One distinctive point associated with forwardstepping is that the order of the reference dynamics is typically specified to be equal to or higher than that of the original nonlinear system, and the reference dynamics and the nonlinear system are governed by a differential/dynamic-cascaded structure. The order invariance or increment of the specified reference dynamics with respect to the nonlinear system and their differential/dynamic-cascaded structure expands significantly the design freedom and thus facilitates the seeking of solutions to many nonlinear control problems which would otherwise often be intractable.
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The algorithm r
elies on computing an upper bound on the supremum of a nonlinear function over a rectangular domain, which has been traditionally done using Bernstein polynomials. We strive to remove the manual step of parallelotope template selection to make the method fully automatic. Furthermore, we show that changing templates dynamically during computations cans improve accuracy. To this end, we investigate two techniques for generating the template directions. The first technique approximates the dynamics as a linear transformation and generates templates using this linear transformation. The second technique uses Principal Component Analysis (PCA) of sample trajectories for generating templates. We have implemented our approach in a Python-based tool called Kaa and improve its performance by two main enhancements. The tool is modular and use two types of global optimization solvers, the first using Bernstein polynomials and the second using NASAs Kodiak nonlinear optimization library. Second, we leverage the natural parallelism of the reachability algorithm and parallelize the Kaa implementation. We demonstrate the improved accuracy of our approach on several standard nonlinear benchmark systems.
This work studies the problem of controlling the probability density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs partial differenti
al equations (PDEs) to model the density evolution and uses density feedback to design control laws which, by acting on individual systems, stabilize their density towards to a target profile. In spite of its stability property and computational efficiency, the success of density feedback relies on assuming the systems to be homogeneous first-order integrators (plus white noise) and ignores higher-order dynamics, making it less applicable in practice. In this work, we present a backstepping design algorithm that extends density control to heterogeneous and higher-order stochastic systems in strict-feedback forms. We show that the strict-feedback form in the individual level corresponds to, in the collective level, a PDE (of densities) distributedly driven by a collection of heterogeneous stochastic systems. The presented backstepping design then starts with a density feedback design for the PDE, followed by a sequence of stabilizing design for the remaining stochastic systems. We present a candidate control law with stability proof and apply it to nonholonomic mobile robots. A simulation is included to verify the effectiveness of the algorithm.
Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of discrete abstractions are based on sampling of both the state and time spaces, which may not be ab
le to guarantee safety for continuous-time systems. In this work, we aim at addressing this problem by considering only state-space abstraction. Firstly, we connect the continuous-time concrete system with its discrete (state-space) abstraction with a control interface. Then, a novel stability notion called controlled globally asymptotic/practical stability with respect to a set is proposed. It is shown that every system, under the condition that there exists an admissible control interface such that the augmented system (composed of the concrete system and its abstraction) can be made controlled globally practically stable with respect to the given set, is approximately simulated by its discrete abstraction. The effectiveness of the proposed results is illustrated by a simulation example.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
