Analysis of switched and hybrid systems - beyond piecewise quadratic methods

This paper presents a method for stability analysis of switched and hybrid systems using polynomial and piecewise polynomial Lyapunov functions. Computation of such functions can be performed using convex optimization, based on the sum of squares decomposition of multivariate polynomials. The analysis yields several improvements over previous methods and opens up new possibilities, including the possibility of treating nonlinear vector fields and/or switching surfaces and parametric robustness analysis in a unified way

Robust Stability Analysis of Nonlinear Hybrid Systems

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems

A new solution approach to polynomial LPV system analysis and synthesis

Based on sum-of-squares (SOS) decomposition, we propose a new solution approach for polynomial LPV system analysis and control synthesis problems. Instead of solving matrix variables over a positive definite cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach

Convex Programs for Temporal Verification of Nonlinear Dynamical Systems

A methodology for safety verification of continuous and hybrid systems using barrier certificates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from the linear programming duality appearing in the discrete shortest path problem, we show in this paper that reachability of continuous systems can also be verified through convex programming. Several convex programs for verifying safety and reachability, as well as other temporal properties such as eventuality, avoidance, and their combinations, are formulated. Some examples are provided to illustrate the application of the proposed methods. Finally, we exploit the convexity of our methods to derive a converse theorem for safety verification using barrier certificates

ANALYSIS FACTORS OF NURSE AND MIDWIFE’S COMMITMENT IN PREVENTION OF MOTHER TO CHILD TRANSMISSION (PMTCT) AT RSUD GAMBIRAN KEDIRI

5% activities of PMTCT prong 1, 2, and 4 was often performed by midwives and nurses in BKIA and Edelwais room. PMTCT as performance was influenced by the commitments, and it had antecedent factors of commitment, based on Allen and Meyer’s Theory (1997). This purpose of this study was to explain the factors that affected the commitment midwives and nurses in RSUD Gambiran Kediri. This research was an analytical descriptive with cross sectional approach. Samples were taken from the total population of midwife and nurse at Edelwais and KIA room. The independent variables wereantecedent factors of commitment, intervining variables were commitments, and dependent variable wasPMTCT. These variables were measured using a questionnaire. This data were analyzed using spearmen rho. The result showed noeffect every antecedent factors of commitment toward commitments with p value >0.05, but there were effect of affective commitment (p=0.004, r=0,885), continuance commitment (p = 0.016, t=-0,803), normative commitment (p=0.028, r=0,762) toward PPIA. It can be concluded that antecedent factors of commitmentdo not affect the commitment, however affective and normative commitment toward PMTCT hadsignificant positive effect and continuance commitment had significant negative effect. Further research could develop this research through the addition of other variables that influence commitment, such as motivation, organizational investment, job satisfaction, job involvement. Keywords: antecedent factors of commitment, organizational commitment, PMTC

ANALYSIS FACTORS OF NURSE AND MIDWIFE’S COMMITMENT IN PREVENTION OF MOTHER TO CHILD TRANSMISSION (PMTCT) AT RSUD GAMBIRAN KEDIRI

5% activities of PMTCT prong 1, 2, and 4 was often performed by midwives and nurses in BKIA and Edelwais room. PMTCT as performance was influenced by the commitments, and it had antecedent factors of commitment, based on Allen and Meyer’s Theory (1997). This purpose of this study was to explain the factors that affected the commitment midwives and nurses in RSUD Gambiran Kediri. This research was an analytical descriptive with cross sectional approach. Samples were taken from the total population of midwife and nurse at Edelwais and KIA room. The independent variables wereantecedent factors of commitment, intervining variables were commitments, and dependent variable wasPMTCT. These variables were measured using a questionnaire. This data were analyzed using spearmen rho. The result showed noeffect every antecedent factors of commitment toward commitments with p value >0.05, but there were effect of affective commitment (p=0.004, r=0,885), continuance commitment (p = 0.016, t=-0,803), normative commitment (p=0.028, r=0,762) toward PPIA. It can be concluded that antecedent factors of commitmentdo not affect the commitment, however affective and normative commitment toward PMTCT hadsignificant positive effect and continuance commitment had significant negative effect. Further research could develop this research through the addition of other variables that influence commitment, such as motivation, organizational investment, job satisfaction, job involvement. Keywords: antecedent factors of commitment, organizational commitment, PMTC

Safety Control Synthesis with Input Limits: a Hybrid Approach

We introduce a hybrid (discrete--continuous) safety controller which enforces strict state and input constraints on a system---but only acts when necessary, preserving transparent operation of the original system within some safe region of the state space. We define this space using a Min-Quadratic Barrier function, which we construct along the equilibrium manifold using the Lyapunov functions which result from linear matrix inequality controller synthesis for locally valid uncertain linearizations. We also introduce the concept of a barrier pair, which makes it easy to extend the approach to include trajectory-based augmentations to the safe region, in the style of LQR-Trees. We demonstrate our controller and barrier pair synthesis method in simulation-based examples.Comment: 6 pages, 7 figures. Accepted for publication at the 2018 American Controls Conference. Copyright IEEE 201

A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates

This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings. In the worst-case setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes it possible to handle nonlinearity, uncertainty, and constraints directly within this framework. In the stochastic setting, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, barrier certificates can be constructed using convex optimization, and hence the method is computationally tractable. Some examples are provided to illustrate the use of the method

Nonlinear control synthesis by convex optimization

A stability criterion for nonlinear systems, recently derived by the third author, can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be interpreted as the stationary density of a substance that is generated all over the state-space and flows along the system trajectories toward the equilibrium. The new criterion has a remarkable convexity property, which in this note is used for controller synthesis via convex optimization. Recent numerical methods for verification of positivity of multivariate polynomials based on sum of squares decompositions are used