On-Line Parameter Estimation for Infinite-Dimensional Dynamical Systems

A novel adaptive algorithm to address the on-line identification of constant uncertain parameters in linear timeinvariant dynamical systems is proposed. The approach can be applied to a broad class of linear dynamical processes including, e.g., delay systems, fractional-order systems, and distributedparameter systems. The proposed scheme takes advantage of a nonlinear adaptation rule inspired by the unit-vector variable-structure control strategy and provides the finite-time parameter estimation. Convergence properties of the algorithm are investigated through Lyapunov analysis, that constructively yields explicit convergence conditions which generalize the wellknown Persistence of Excitation (P.E.) and identifiability requirements arising in conventional adaptive estimation. The theoretical findings are substantiated by extensive simulation examples.

Parameter identification for nonlinear systems: Guaranteed confidence regions through LSCR

This paper presents a method for recursively estimating the static parameters of linear or nonlinear stochastic dynamic systems given the systems' inputs and outputs. The paper accomplishes this objective by combining polynomial chaos theory with maximum likelihood estimation. The parameter estimates are calculated in a recursive or iterative manner. To the best of the author's knowledge, this is the first paper to address recursive maximum likelihood parameter estimation using polynomial chaos theory. The proposed approach is demonstrated on two systems: a linear 2nd order system with unknown damping and natural frequency, and a nonlinear Van der Pol oscillator with an unknown nonlinear damping coefficient. Because this recursive estimator is applicable to nonlinear systems, the authors portend that this novel formulation will be useful for a broad range of estimation problems.

This work presents a new strategy in design optimization of nonlinear vibration absorbers with continuous and discontinuous motions. A cluster-based harmonic balance aided optimization technique using force balance or energy balance as the basis is generalized and adapted for nonlinear systems. It is found that optimal design parameters form a cluster in the parameter space and points from the parameter space inside the cluster satisfies design considerations. One of the main disadvantages of using existing optimization methods in nonlinear systems is that the parameter regimes, which provide periodic solutions, are not known beforehand, so one has to first do bifurcation studies to arrive at periodic regimes and optimization has to be conducted in the range. Proposed method combines these two steps as it converges to periodic clusters alone. Since the method admits only periodic solutions, occurrence of conditions such as chaos and quasi periodicity can be eliminated from the dynamics of the system. The proposed method can also be used to find the optimal parameters of both linear and nonlinear dynamical systems.

System modeling and parameter identification of micro aerial vehicles (MAV) are crucial for robust autonomy, especially under highly dynamic motions. Visual-inertial-aided online parameter identification has recently seen research attention due to the demanding of adaptation to platform configuration changes with minimal onboard sensor requirements. To this end, we design an online MAV system identification algorithm to tightly fuse visual, inertial and MAV aerodynamic information within a lightweight multi-state constraint Kalman filter (MSCKF) framework. In particular, while one could blindly fuse the MAV dynamic-induced relative motion constraints in EKF, we numerically show that due to the (quadrotor) MAV system modeling inaccuracy, they often become overconfident and negatively impact the state estimates. As such, we leverage the Schmidt-Kalman filter (SKF) for MAV system parameter identification to prevent corruption of state estimates. Through extensive simulations and real-world experiments, we validate the proposed SKF-based scheme and demonstrate its ability to perform robust system identification even in the presence of an inconsistent MAV dynamic model under different motions.

This paper describes and compares the application of two alternative approaches to the identification of linear systems from input-output data. The first approach is based on fitting input and output data by sums of exponentials and deriving both the system structure and the parameter values from the resulting functions. The second approach is based on assuming a differential-equation structure and finding only the parameter values from the given data. The relative advantages, disadvantages, and computational aspects of both approaches are discussed with reference to a specific biological problem. The results are applicable to a variety of engineering and scientific problems described by systems of first-order linear differential equations.

The present paper develops an enhanced response sensitivity approach for parameter identification of nonlinear time-delay systems from the time-domain data. Accurate and rapid identification of the time-delay system’s parameters is the key to achieve effective control and synchronization, especially for the delay parameters. The work of this paper is mainly threefold. Firstly, taking a general nonlinear time-delay system as the investigated object, the characteristics of the nonlinear time-delay system are introduced, and the response sensitivity analysis with respect to the system parameters is derived. Then, the problem of parameter identification is modeled as a nonlinear least-squares optimization function. To this end, a novel iteration-based approach is developed to solve such problem, and the ill-posed situation is tackled by Tikhonov regularization. Besides, the trust-region constraint is implemented to enhance the convergence of the algorithm. Finally, the feasibility of the proposed approach is verified by two numerical examples and a real electronic circuit experiment. The results proved that the proposed approach can identify parameters of nonlinear time-delay systems accurately, robustly and effectively.

We present the results of analytical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing nonequilibrium processes ranging from aggregation phenomena to the cooperation of individuals. On tuning the initial conditions, a dynamical transition with a universal scaling behavior is observed between two different asymptotic (in time) solutions. The scaling behavior at the transition is also obtained in a self-organized manner, independent of the initial conditions, on temporally evolving the diffusion equation subjected to a mirror symmetry transformation.

The differential migration of ions in an applied electric field is the basis for separation of chemical species by capillary electrophoresis. Axial diffusion of the concentration peak limits the separation efficiency. Electromigration dispersion is observed when the concentration of sample ions is comparable to that of the background ions. Under such conditions, the local electrical conductivity is significantly altered in the sample zone making the electric field, and therefore, the ion migration velocity concentration dependent. The resulting nonlinear wave exhibits shock like features, and, under certain simplifying assumptions, is described by Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 201072, pg. 2047). In this paper, we consider the more general situation where the walls of the separation channel may have a non-zero zeta potential and are therefore able to sustain an electro-osmotic bulk flow. The main result is a one dimensional nonlinear advection diffusion equation for the area averaged concentration. This homogenized equation accounts for the Taylor-Aris dispersion resulting from the variation in the electro-osmotic slip velocity along the wall. It is shown that in a certain range of parameters, the electro-osmotic flow can actually reduce the total dispersion by delaying the formation of a concentration shock. However, if the electro-osmotic flow is sufficiently high, the total dispersion is increased because of the Taylor-Aris contribution.

Various versions are compared of the multidimensional method of orthogonal regression in the problem of estimating the parameters of linear systems by short sections of transient processes with additive measuring perturbations. The methods are classified by the degree of the use of information on linear links between counts of trajectories of a dynamic object.

Construction of approximate reasoning model for dynamic CPS network and system parameter identification

An algebraic approach to the identification of parameters in linear infinite dimensional systems is proposed. It is based on operational calculus. First, the method is derived for a system with delayed input and homogeneous initial conditions. A similar approach is applicable to systems described by linear partial differential equations. This is discussed for second order p.d.e., in particular for the one dimensional heat equation.

Identification of fractional order non– homogeneous Hammerstein-Wiener MISO continuous systems

An improved position estimation of the sensorless control system with online parameter identification based on back-Electromotive Force (EMF) voltage is presented for the dual-winding fault-tolerant permanent magnet motor (FTPMM). In this control system, the rotor position is estimated by the flux linkage and the back-EMF which are generated by each phase winding. By introducing phase-locked loop technology to compensate the steady-state error of the system and online identification of motor parameters which is using the least-square method with forgetting factor, more accurate position estimation can be obtained. The current vector fault-tolerant control strategy improves the fault tolerance of the system and makes it strong robust stability. The simulation results have shown that the accurate position data can be acquired both under healthy condition and single-phase fault condition. Then, the hardware experimental results show the feasibility and validity of the proposed algorithm.

This paper addresses the problem of computing controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. We develop new methods for models of systems subject to both stochastic and parametric uncertainties. We provide for the first time novel simulation relations for enabling correct-by-design control refinement, that are founded on coupling uncertainties of stochastic systems via sub-probability measures. Such new relations are essential for constructing abstract models that are related to not only one model but to a set of parameterized models. We provide theoretical results for establishing this new class of relations and the associated closeness guarantees for both linear and nonlinear parametric systems with additive Gaussian uncertainty. The results are demonstrated on a linear model and the nonlinear model of the Van der Pol Oscillator.