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Continuous time nonlinear dynamical system states variables estimated suboptimally from discrete noisy measurements with second order nonlinear filter, deriving dynamical equations
Continuous time nonlinear dynamical system states variables estimated suboptimally from discrete noisy measurements with second order nonlinear filter, deriving dynamical equations
The vestibulo-ocular reflex (VOR) is a well-known dual mode bifurcating system that consists of slow and fast modes associated with nystagmus and saccade, respectively. Estimation of continuous-time parameters of nystagmus and saccade models are known to be sensitive to estimation methodology, noise and sampling rate. The stable and accurate estimation of these parameters are critical for accurate disease modelling, clinical diagnosis, robotic control strategies, mission planning for space exploration and pilot safety, etc. This paper presents a novel indirect system identification method for the estimation of continuous-time parameters of VOR employing standardised least-squares with dual sampling rates in a sparse structure. This approach permits the stable and simultaneous estimation of both nystagmus and saccade data. The efficacy of this approach is demonstrated via simulation of a continuous-time model of VOR with typical parameters found in clinical studies and in the presence of output additive noise.
This paper presents a hybrid state-space self-tuning control scheme using dual-rate sampling for suboptimal digital adaptive control of linear time-invariant continuous-time multivariable stochastic systems with unknown parameters. An equivalent fast-rate discrete-time state-space innovation model (with estimated states) of the continuous-time system is constructed by using the estimated system parameters and Kalman gain. To utilize the existing optimal regional-pole assignment method developed in the continuous-time domain, the constructed fast-rate discrete-time model is converted into an equivalent continuous-time model for the development of a state-feedback optimal control law with pole placement in a specific region. The developed analog optimal control law is then converted into an equivalent pseudo-slow-rate digital control law via the proposed digital redesign technique, which can be realized via slow-rate digital electronics. The proposed method enables the development of a digitally implementable advanced control algorithm for digital adaptive control of continuous-time multivariable stochastic systems which may be unstable and/or have nonminimum phase.
This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are established to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.
In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.
Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.
The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.
The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Liapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.
The input/output characteristics of an ultrasonic testing system used for stress wave factor measurements were studied. The fundamentals of digital signal processing are summarized. The inputs and outputs are digitized and processed in a microcomputer using digital signal processing techniques. The entire ultrasonic test system, including transducers and all electronic components, is modeled as a discrete-time linear shift-invariant system. Then the impulse response and frequency response of the continuous time ultrasonic test system are estimated by interpolating the defining points in the unit sample response and frequency response of the discrete time system. It is found that the ultrasonic test system behaves as a linear phase bandpass filter. Good results were obtained for rectangular pulse inputs of various amplitudes and durations and for tone burst inputs whose center frequencies are within the passband of the test system and for single cycle inputs of various amplitudes. The input/output limits on the linearity of the system are determined.
State estimation is a fundamental part of monitoring, control, and real-time optimization in continuous pharmaceutical manufacturing. For nonlinear dynamic systems with hard constraints, moving horizon estimation (MHE) can estimate the current state by solving a well-defined optimization problem where process complexities are explicitly considered as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, state estimates can be unreliable if noise is not normally distributed or measurements are contaminated with gross or systematic errors. In this paper, to improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE framework. The proposed MHE approach is implemented on two pharmaceutical continuous feeding–blending system (FBS) configurations which include loss-in-weight (LIW) feeders and continuous blenders. Numerical results show that our MHE approach is robust to gross errors and can provide reliable state estimates when measurements are contaminated with outliers and drifts. Finally and moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.
Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.
Time-domain methods for the design of recursive digital filters using a squared error criterion are compared with a frequency-domain technique. Levy's method, which has been used to estimate transfer functions of continuous-time systems is modified to obtain design equations for digital filters. A special case of Levy's method is shown to be essentially equivalent to the time-domain methods.
A survey is presented of some of the approaches which have been considered in freight demand estimation. The few existing continuous time computer simulations of aviation systems are reviewed, with a view toward the assessment of this approach as a tool for structuring air freight studies and for relating the different components of the air freight system. The variety of available data types and sources, without which the calibration, validation and the testing of both modal split and simulation models would be impossible are also reviewed.
Optical ranging is a problem of estimating the round-trip flight time of a phase- or amplitude-modulated optical beam that reflects off of a target. Frequency- modulated, continuous-wave (FMCW) ranging systems obtain this estimate by performing an interferometric measurement between a local frequency- modulated laser beam and a delayed copy returning from the target. The range estimate is formed by mixing the target-return field with the local reference field on a beamsplitter and detecting the resultant beat modulation. In conventional FMCW ranging, the source modulation is linear in instantaneous frequency, the reference-arm field has many more photons than the target-return field, and the time-of-flight estimate is generated by balanced difference- detection of the beamsplitter output, followed by a frequency-domain peak search. This work focused on determining the maximum-likelihood (ML) estimation algorithm when continuous-time photoncounting detectors are used. It is founded on a rigorous statistical characterization of the (random) photoelectron emission times as a function of the incident optical field, including the deleterious effects caused by dark current and dead time. These statistics enable derivation of the Cramér-Rao lower bound (CRB) on the accuracy of FMCW ranging, and derivation of the ML estimator, whose performance approaches this bound at high photon flux. The estimation algorithm was developed, and its optimality properties were shown in simulation. Experimental data show that it performs better than the conventional estimation algorithms used. The demonstrated improvement is a factor of 1.414 over frequency-domainbased estimation. If the target interrogating photons and the local reference field photons are costed equally, the optimal allocation of photons between these two arms is to have them equally distributed. This is different than the state of the art, in which the local field is stronger than the target return. The optimal processing of the photocurrent processes at the outputs of the two detectors is to perform log-matched filtering followed by a summation and peak detection. This implies that neither difference detection, nor Fourier-domain peak detection, which are the staples of the state-of-the-art systems, is optimal when a weak local oscillator is employed.
The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.
This paper presents a hybrid state-space self-tuning design methodology using dual-rate sampling for suboptimal digital adaptive control of attitude and momentum management for the Space Station. This new hybrid adaptive control scheme combines an on-line recursive estimation algorithm for indirectly identifying the parameters of a continuous-time system from the available fast-rate sampled data of the inputs and states and a controller synthesis algorithm for indirectly finding the slow-rate suboptimal digital controller from the designed optimal analog controller. The proposed method enables the development of digitally implementable control algorithms for the robust control of Space Station Freedom with unknown environmental disturbances and slowly time-varying dynamics.
Assurance cases are being increasingly acknowledged as a way to build trust in complex systems with autonomous capabilities [1]. An assurance case is a comprehensive, defensible, and valid justification that a system will function as intended for the specific mission and operating environment. Such justifications for systems with autonomous capabilities are often based on various probabilistic quantifications [2]. Due to the dynamic nature of the environmental conditions in which these systems operate, as well as the changing nature of the autonomous systems themselves, these probabilistic quantifications cannot be simply estimated once during design time. Rather, they need to be continually evaluated during systems operations to ensure that the assurance case justifications are valid. We refer to the assurance case that combines both the static and dynamic elements as a Dynamic Assurance Case (DAC). Such complex systems with autonomous capabilities are often deployed with a Ground Control Software (GCS) component to enable remote operation. Whether the system is composed of a single unit or a fleet of units, deployed distributed or in remote environments, GCS acts as a window into the behavior of the deployed system. It receives telemetry from the system, issues commands to the system and provides various functionalities to visualize the system performance. We propose a dynamic assurance framework where the GCS acts as a relay between the autonomous system and its DAC. GCS can be used to measure both unit-specific as well as system-wide probabilistic quantifications using the incoming telemetry. We embed these quantifications throughout the DAC as variables that can be updated by external sources. We use the GCS to periodically update these variables, which allows us to continually evaluate the formally defined assurance case justifications. We demonstrate our dynamic assurance framework in the NASA Ames project Troupe1 that aims at developing a fleet of rovers capable of au- tonomously mapping their environment. The rovers work cooperatively, each collecting data for different parts of the environment. Each rover runs an identical core Flight System (cFS) [4] application. Troupe1 uses OpenC3 Cosmos [5] as the ground system, and AdvoCATE [3] to capture the system DAC. We show how we can measure both rover-specific and system-wide quantifications in Cosmos using its Ruby scripting editor and pass them into the DAC modelled in AdvoCATE. Then, we show how these incoming variables can be embedded in different parts of the DAC and how effects of their updates can be observed