Switched Systems with Transient Unsustainable Modes

Non-weighted H∞ performance for 2-D FMLSS switched system with maximum and minimum dwell time

Purpose Applicator-based dose optimization (forward planning) emphasizes dwell time homogeneity to avoid regions of exceptionally high dose concentration. Anatomy-based dose optimization (inverse planning) relaxes this constraint in order to obtain a dose distribution that is more conformal the anatomy. We developed a version of inverse planning constrained by maximum dwell times. The relationship between dwell time homogeneity and the dose delivered to cancerous and healthy organs is examined. Methods and Materials A software method was implemented within the IPSA inverse planning algorithm to allow for (1) imposition of a user-defined global maximum dwell time at any given dwell position and (2) homogeneity of dwell times within any given catheter. In-silico studies were performed on six previously-treated-patient image datasets using the contours and catheter digitization of the clinically-used plan. Two each of tandem-and-ring gynecological, tandem-and-ovoid gynecological, and prostate were examined. The plan used for treatment served as the control and had no restriction on dwell times. New plans were optimized by imposing either a global (Study 1) or catheter-specific maximum dwell times (Study 2) for different time limits. Dosimetric indices were compared with the control plans. Results Clinically acceptable plans were achievable with modest restriction of the dwell times, but severe restriction lead to unacceptable plans. Across all studies, restriction of dwell times correlated with an increase of the final objective function value. A higher objective function means less adherence of the optimization to the dosimetric requirements imposed on the optimization by the user. Conclusion Imposing restrictions on a global maximum dwell and intra-catheter dwell time homogeneity necessarily results in a worsening of the dosimetric optimization objective function. However, less severe restrictions can allow for some tailoring of the dose distribution to avoid intra-catheter dwell time heterogeneity with only a small decrease in target coverage. Research sponsored in part by Nucletron.

This work presents an investigation of the minimum dwell time during the precision cylindrical-plunge grinding process. According to the model of acoustic emissions proposed in earlier work, two estimation algorithms of the dwell time, focused on the size error and the surface roundness of the machined workpiece, are deduced from the models of the material removal and the surface roundness, respectively. Based on the proposed estimation algorithms, an on-line estimation method of the minimum dwell time is developed using the measurement and analysis of the acoustic emission signal. A series of experiments of grinding C45 steel are conducted to confirm the validity of the proposed estimation algorithms and determine the model coefficient. The ability of the estimation algorithms to predict the minimum dwell time is deemed necessary for optimal control of the grinding process. In addition, the proposed model provides a new approach to estimate the machined qualities of a workpiece such as the surface roughness and size error using the dwell time of the grinding process.

The aim of approximate model predictive control (MPC) is to alleviate the computational cost by learning an explicit control policy using data generated from offline solutions to MPC problems. However, directly constructing a neural network using these input‐output data cannot guarantee learning efficiency or constraint satisfaction. This study integrates prior knowledge from solving MPC optimization problems into the construction and training of a neural network‐based approximate controller, proposing a knowledge‐driven approximate MPC scheme. First, by designing a differentiable optimization layer, the constraints of the optimization problem are embedded into the neural network structure, ensuring that the generated approximate control inputs satisfy the constraints. Subsequently, derivative information is explicitly incorporated into the neural network, and a new loss function is designed, effectively reflecting the characteristics of the optimization problem during training. Finally, to ensure that the neural network meets performance requirements when approximating the MPC controller, statistical validation techniques are used for a posteriori evaluation of the accuracy of the resulting approximate controller. Through simulation examples, we demonstrate the significant potential of this method as an approximation for predictive control laws. Compared to existing methods, this new approach proves to achieve efficient learning while ensuring constraint satisfaction.

We present cascading dwell gaze typing, a novel approach to dwell-based eye typing that dynamically adjusts the dwell time of keys in an on-screen keyboard based on the likelihood that a key will be selected next, and the location of the key on the keyboard. Our approach makes unlikely keys more difficult to select and likely keys easier to select by increasing and decreasing their required dwell times, respectively. To maintain a smooth typing rhythm for the user, we cascade the dwell time of likely keys, slowly decreasing the minimum allowable dwell time as a user enters text. Cascading the dwell time affords users the benefits of faster dwell times while causing little disruption to users' typing cadence. Results from a longitudinal study with 17 non-disabled participants show that our dynamic cascading dwell technique was significantly faster than a static dwell approach. Participants were able to achieve typing speeds of 12.39 WPM on average with our cascading technique, whereas participants were able to achieve typing speeds of 10.62 WPM on average with a static dwell time approach. In a small evaluation conducted with five people with ALS, participants achieved average typing speeds of 9.51 WPM with our cascading dwell approach. These results show that our dynamic cascading dwell technique has the potential to improve gaze typing for users with and without disabilities.

Tailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to epsilon -optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions.

Explicit conditions on the minimum dwell time that guarantees the asymptotic stability of switched linear systems are given. To this aim, methods that have been proposed for non-defective stable subsystem matrices are generalized to arbitrary stable subsystems matrices. Admissible switchings between subsystems are assumed to be in a general form, namely switchings respect a given directed graph. It is shown that logarithmic norm of matrix exponentials and Lambert-W functions can be used to bound the solutions of switched linear systems in case of defective subsystem matrices. Using a generalized version of Jordan form, dwell time bound can be found for any set of stable subsystem matrices.

In this paper, the consensus problem of a class of linear multi-agent systems is analysed. In our model, switching between subnetworks and competition between agents is considered simultaneously. We suppose that all subnetworks cannot achieve a consensus and switching signal has a minimum dwell time. By using the time-dependent quadratic Lyapunov function and the average dwell time method, a consensus condition of switched networks is obtained. By using the sum of squares (SOS) programming in the software package SOSTOOLS of Matlab, these resulting conditions can be implemented. The results obtained are also extended to uncertain linear multi-agent systems. Finally, a simulation example is given to illustrate the validity of our results.

Robust stability of switched positive linear systems with interval uncertainties via multiple time-varying linear copositive Lyapunov functions

SummaryThis article is concerned with the quasi‐time‐dependent asynchronous filter design problem for a class of discrete‐time switched systems via the event‐triggering mechanism. Applying the quasi‐time‐dependent Lyapunov functions and the mode‐dependent average dwell time technique, an asynchronous filter is designed with a weighted performance index; the filter parameter matrices are quasi‐time‐dependent in each event‐triggering‐dependent sampling interval; both cases (Case 1: no more than one switching, Case 2: multiple switchings) are taken into account in this sampling interval, by which the assumption, that the maximal asynchronous period is not larger than the minimal dwell time, is relaxed in this article. Simulation examples are given to show the less conservatism and effectiveness of the proposed results.

Compression-induced destabilization was investigated in various celecoxib amorphous solid dispersions containing hydroxypropyl methylcellulose (HPMC), poly(vinylpyrrolidone)/vinyl acetate copolymer (PVP/VA), or poly(vinylpyrrolidone) (PVP) at a concentration range of 1-10% w/w. Pharmaceutically relevant (125 MPa pressure with a minimal dwell time) and extreme (500 MPa pressure with a 60 s dwell time) compression conditions were applied to these systems, and the changes in their physical stability were monitored retrospectively (i.e., in the supercooled state) using dynamic differential scanning calorimetry (DSC) and low-frequency Raman (LFR) measurements over a broad temperature range (-90 to 200 and -150 to 140 °C, respectively). Both techniques revealed similar changes in the crystallization behavior between samples, where the application of a higher compression force of 500 MPa resulted in a more pronounced destabilization effect that was progressively mitigated with increasing polymer content. However, other aspects such as more favorable intermolecular interactions did not appear to have any effect on reducing this undesirable effect. Additionally, for the first time, LFR spectroscopy was used as a viable technique to determine the secondary or local glass-transition temperature, Tg,β, a major indicator of the physical stability of neat amorphous pharmaceutical systems.

This work outlines a practical process, based on dwell times, for ensuring the stability of non-linear switched systems with a different stable equilibrium for each mode. Relevant Lyapunov theorems are discussed, followed by a derivation of an algorithm that determines dwell times for each system mode for guaranteeing stability. An analysis of algorithm parameters and potentially troublesome systems is then included. Finally, two examples are drawn from power electronics and electric machinery and processed by the proposed method. Application of this approach will both grant confidence in switched system stability and warn of possible unstable system behavior when appropriate.

The need for cost-effective fuel economy improvements has driven the introduction of automatic transmissions with an increasing number of gear ratios. Incorporation of interlocking dog clutches in these transmissions decreases package space and increases efficiency, as compared to conventional dry or wet clutches. Unlike friction based clutches, interlocking dog clutches require very precise rotational speed matching prior to engagement. Precise engine speed control is therefore critical to maintaining high shift quality. This research focuses on controlling the engine speed during a gearshift period by manipulating throttle position and combustion phasing. Model predictive control (MPC) is advantageous in this application since the speed profile of a future prediction horizon is known with relatively high confidence. The MPC can find the optimal control actions to achieve the designated speed target without invoking unnecessary actuator manipulation and violating hardware and combustion constraints. This research utilizes linear parameter varying (LPV) MPC to control the engine speed during the gearshift period. Combustion stability constraints are considered with a control oriented covariance of indicated mean effective pressure model (COV of IMEP). The proposed MPC engine speed controller is validated with a high-fidelity 0-dimensional engine model with crank angle resolution. Four case studies, based on simulation, investigate the impact of different MPC design parameters. They also demonstrate that the proposed MPC engine controller successfully achieves the speed reference tracking objective while considering combustion variation constraints.

Advanced control techniques for CHP-DH systems: A critical comparison of Model Predictive Control and Reinforcement Learning

The thermal behavior of semiconductor devices of voltage source inverters for a traction frequency converter and its control systems are investigated. A test bed for studying thermal processes in steady state and transient modes occurring in semiconductor modules with air forced cooling systems is described. The results of an experimental investigation for the Infineon FF300R06KE3 module are analyzed and compared to the results of a mathematical model. Transfer functions of a semiconductor module as an object of temperature control are synthesized with respect to the collector current, cooling air flow, and frequency switching. The control system of thermal behavior of a voltage source inverter with two control actions on the object of temperature control (cooling air flow and frequency switching) is developed. It is proposed to use an electric drive with an induction motor and scalar control system for the purposes of regulating the cooling air flow. The effectiveness of the proposed control system is confirmed by means of simulation in MATLAB/Simulink in transient and steady-state modes.