Linear Continuous Time Research Articles

Constructing Lyapunov–Krasovskii functionals for linear positive continuous time difference systems

Abstract In this paper, a linear positive functional difference system with discrete and distributed delays is studied. It is proved that if the considered system is exponentially stable, then it admits both linear and diagonal quadratic Lyapunov–Krasovskii functionals. In addition, new exponential stability conditions for switched linear positive functional difference systems are obtained on the basis of a constructive approach to the design of common Lyapunov–Krasovskii functionals for the associated families of subsystems.

Online Policy Iteration Algorithms for Linear Continuous-Time H-Infinity Regulation With Completely Unknown Dynamics

Online Policy Iteration Algorithms for Linear Continuous-Time H-Infinity Regulation With Completely Unknown Dynamics

Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties

This study develops robust recursive least-squares (RLS) fixed-point smoothing and filtering algorithms for signals in linear continuous-time stochastic systems with uncertainties. The algorithms use covariance information, such as the cross-covariance function of the signal with the observed value and the autocovariance function of the degraded signal. A finite Fourier cosine series expansion approximates these functions. Additive white Gaussian noise is present in the observation of the degraded signal. A numerical simulation compares the estimation accuracy of the proposed robust RLS filter with the robust RLS Wiener filter, showing similar mean square values (MSVs) of the filtering errors. The MSVs of the proposed robust RLS fixed-point smoother are also compared to those of the proposed robust RLS filter.

Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems

This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method.

Distributed Robust Control Design for Multi-Intelligent Body Systems Based on KYP Lemma

Abstract In this paper, a distributed robust control system is analyzed and investigated, and a series of control applications of the system are discussed using KYP primitives. Reliable H ∞ -state feedback and output feedback controllers are given for linear continuous time, ensuring that the corresponding closed-loop system is asymptotically stable and satisfies full-frequency performance. Simulation examples verify the superiority of the methodology of this paper, and the level of noise rejection is further enhanced as the number h of measured output values used is increased. The optimal performance metrics for finite-frequency are all lower than full-frequency, and the distributed filter outperforms the conventional filter. The closed-loop system has a maximum magnitude of 5.480 and 9.075, which meet the robustness requirement for the 4-8 Hz frequency range. The time-lag system can return to its stable state about 4 seconds after the disturbance, ensuring good, robust stability. The distributed robust control system proposed in this paper achieves good practical application results, and the numerical examples demonstrate the method’s effectiveness.

Observer-based Control for Linear Continuous-Time Systems with Fully Homomorphic Encryption

Observer-based Control for Linear Continuous-Time Systems with Fully Homomorphic Encryption

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-Time System Identification

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-Time System Identification

Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems

Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems

Policy Iteration-Based Learning Design for Linear Continuous-Time Systems Under Initial Stabilizing OPFB Policy.

Policy iteration (PI), an iterative method in reinforcement learning, has the merit of interactions with a little-known environment to learn a decision law through policy evaluation and improvement. However, the existing PI-based results for output-feedback (OPFB) continuous-time systems relied heavily on an initial stabilizing full state-feedback (FSFB) policy. It thus raises the question of violating the OPFB principle. This article addresses such a question and establishes the PI under an initial stabilizing OPFB policy. We prove that an off-policy Bellman equation can transform any OPFB policy into an FSFB policy. Based on this transformation property, we revise the traditional PI by appending an additional iteration, which turns out to be efficient in approximating the optimal control under the initial OPFB policy. We show the effectiveness of the proposed learning methods through theoretical analysis and a case study.

Analysis of the pointwise completeness and the pointwise degeneracy of the standard and fractional descriptor linear systems and electrical circuits

The Drazin inverse of matrices is applied to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor standard and fractional linear continuous-time and discrete-time systems. It is shown that: 1) The descriptor linear continuous-time system is pointwise complete if and only if the initial and final states belong to the same subspace. 2) The descriptor linear discrete-time system is not pointwise complete if its system matrix is singular. 3) System obtained by discretization of continuous-time system is always not pointwise complete. 4) The descriptor linear continuous-time system is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. 5) The descriptor fractional system is pointwise complete if the matrix defined by (36) is invertible. 6) The descriptor fractional system is pointwise degenerated if and only if the condition (41) is satisfied. Considerations are illustrated by examples of descriptor linear electrical circuits.

Predefined-time synchronization for competitive neural networks with different time scales and external disturbances

This paper presents a study on the predefined-time (PdT) and practical PdT synchronization of competitive neural networks (CNN) in the presence of different time scales and external disturbances. Two types of external disturbances, which satisfy Lipschitz or bounded conditions, are investigated respectively. The new PdT and practical PdT stability theorems are derived in singularly perturbed systems, where the final residual set is given in detail. By employing the newly derived stability theorems, novel autonomous controllers are designed without relying on a continuous linear term and time scale parameters, while enabling PdT or practical PdT synchronization for drive-response CNNs. Additionally, upper bounds for the settling time are estimated, allowing for adjusting the predefined synchronization times regardless of the initial conditions. Finally, numerical simulations are conducted to demonstrate the effectiveness of the main results.

An effective controller design strategy for higher order systems

The recent methods that guarantee the stability of the reduced-order models are Mihailov stability, improved Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization. Further, these methods could overcome the limitations such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. This research emphasizes the design of the proposed compensating algorithm by using an additional open loop zero for the stable reduced-order models of large-scale single-input single-output linear time-invariant continuous time systems. The results of the proposed algorithm are compared with the existing compensating methods and the design is validated and illustrated numerically.

Event-Triggered Optimal Adaptive Control of Partially Unknown Linear Continuous-Time Systems With State Delay

Event-Triggered Optimal Adaptive Control of Partially Unknown Linear Continuous-Time Systems With State Delay

Hypocoercivity and hypocontractivity concepts for linear dynamical systems

For linear dynamical systems (in continuous-time and discrete-time), we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as well as (semi-)dissipativity and (semi-)contractivity, respectively. On the basis of these results, the short-time behavior of the propagator norm for linear continuous-time and discrete-time systems is characterized by the (shifted) hypocoercivity index and the (scaled) hypocontractivity index, respectively.

Preview Repetitive Control for Linear Continuous-time System

Preview Repetitive Control for Linear Continuous-time System

Parameter Estimation Methods of Linear Continuous-Time Time-Delay Systems from Multi-frequency Response Data

Parameter Estimation Methods of Linear Continuous-Time Time-Delay Systems from Multi-frequency Response Data

An EOQ model for deteriorating item with continuous linear time dependent demand with trade of credit and replenishment time being demand dependent

This study is about an inventory model with continuous linear time dependent demand rate with constant rate of deterioration in the consideration of partial backorder including delay in payment and time period is demand dependent. Demand is the fundamental attribute for consideration of inventory related problem. In reality, there is some inter connection of demand function among various time interval for which the demand cannot change drastically at some critical point during the appearance of another state of system. Thus, it is quite natural that the demand function should be continuous in nature in inventory management problem. So, here the most prominent part of our present study is the consideration of time dependent continuous demand in the proposed model. A supportive numerical example of the proposed model is illustrated for insightful investigation. The solution method and sensitivity analysis has also been presented.

Regulator Problem for Linear Continuous-Time Delay Dynamical Systems With Symmetrical Constrained Control

Regulator Problem for Linear Continuous-Time Delay Dynamical Systems With Symmetrical Constrained Control

Scraton Method for Solving nth Order State-Space Equations of Linear Continuous-Time Control Systems

The paper presents a developed method with algorithms written in Matlab language to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using Scraton method. State-space equation is the modern representation to analysis continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order Scraton method. Scraton method employed to find the output values of the state-space equations. Comparisons between the numerical and exact results are given for some numerical examples to conciliate the accuracy of the proposed method.

Raising the bar for patient experience during care transitions in Canada: A repeated cross-sectional survey evaluating a patient-oriented discharge summary at Ontario hospitals.

Patient experience when transitioning home from hospital is an important quality metric linked to improved patient outcomes. We evaluated the impact of a hospital-based care transition intervention, patient-oriented discharge summary (PODS), on patient experience across Ontario acute care hospitals. We used a repeated cross-sectional study design to compare yearly positive (top-box) responses to four questions centered on discharge communication from the Canadian Patient Experience Survey (2016-2020) among three hospital cohorts with various levels of PODS implementation. Generalized Estimating Equations using a binomial likelihood accounting for site level clustering was used to assess continuous linear time trends among cohorts and cohort differences during the post-implementation period. This research had oversight from a public advisory group of patient and caregiver partners from across the province. 512,288 individual responses were included. Compared to non-implementation hospitals, hospitals with full implementation (>50% discharges) reported higher odds for having discussed the help needed when leaving hospital (OR = 1.18, 95% CI = 1.02-1.37) and having received information in writing about what symptoms to look out for (OR = 1.44, 95% = 1.17-1.78) post-implementation. The linear time trend was also significant when comparing hospitals with full versus no implementation for having received information in writing about what symptoms to look out for (OR = 1.05, 95% CI = 1.01-1.09). PODS implementation was associated with higher odds of positive patient experience, particularly for questions focused on discharge planning. Further efforts should center on discharge management, specifically: understanding of medications and what to do if worried once home.