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The integrated energy system is widely acknowledged as an effective method for advancing the adoption of renewable energy sources and reducing carbon emissions. To address economic issues caused by the inconsistency between traditional single-stage planning capacities of the park-level integrated energy system (PIES), the long-term planning model is proposed, which consists of multi-stage divisions and incorporates the ladder-type carbon trading mechanism. The model utilizes the long-term, multi-stage planning approach to determine the optimal installed capacity of equipment. Meanwhile, the ladder-type carbon trading mechanism is conducted considering the relationship between actual carbon emissions, carbon emission quotas, and carbon trading cost. The study assesses the impact of carbon trading mechanisms and various planning stage divisions on the economic feasibility of the PIES and its ability to reduce carbon emissions. The results indicate that compared to fixed carbon price trading strategies, the implementation of ladder-type carbon trading increases costs by 0.15 %–0.18 %, but reduces carbon emissions by 0.36 %–0.6 %; as the number of planning stages increases, carbon emissions significantly decrease, and lifecycle costs also significantly decrease. Compared to traditional single-stage planning, carbon emissions decrease by 14.6 % and lifecycle costs decrease by 15.17 % at number of planning stage K = 15; when the baseline price is set at 0.5 yuan/kg and the price growth rate is 0.5, the optimal values of carbon emissions and carbon trading cost are achieved. In conclusion, this study serves as references for the strategic implementations of PIES, emphasizing the importance of economic efficiency and low-carbon practices in line with the system's long-term development and sustainability objectives.

A Coiflet-type wavelet-homotopy approach is implemented to investigate the large deformation of a circular plate resting on different nonlinear foundations with various boundary parameters. A parameterized and continuous boundary model for circular plate with various constraints of rotation and translation has been proposed overlooked in previous studies. Parameterized wavelet approximation of arbitrary Robin-type boundary is reconstituted without variable substitution. Comprehensive analysis on the parameterized Robin-type boundaries is conducted by Linear Programming Approach, indicating the boundary singularities are actually false corresponding to the degenerated cases of Dirichlet-type and Neumann-type ones. Highly accurate Coiflet-type solutions of the coupled governing nonlinear differential equations with integration involving in extreme bending of circular plate have been obtained performing good computational efficiency in excellent agreement with other numerical results, which implies the wavelet scheme is a high precision computation method with great potential in giving highly accurate solutions of strongly nonlinear problems. • The new Coiflet-type wavelet approach for Robin boundary conditions is proposed. • Extreme large bending of a circular plate resting nonlinear foundations is analyzed. • Highly accurate solutions with integrations and singularities are obtained. • Parameterized Robin-type boundaries are conducted by Linear Programming Approach. • Validity and efficiency of the proposed technique is provided. [ABSTRACT FROM AUTHOR]

In this study, the design problem of multiple‐mode observer and multiple‐mode controller is studied for switched positive linear systems. By proposing a new design approach for a class of switched positive linear system, numerical conditions for the existence of multiple‐mode observer and multiple‐mode controller are presented by using linear programming approach. First, a multiple‐mode observer is designed such that the error system is exponentially stable. Next, a robust multiple‐mode interval observer is presented for uncertain switched positive systems with uncertain parameters. In the sequel, a multiple‐mode output‐feedback controller is designed such that the closed‐loop system is exponentially stable. Compared with the existing references, the design method can bring out lower computational burden. Finally, three examples are given to show the effectiveness of the authors' results. [ABSTRACT FROM AUTHOR]

In this study, the authors analyse the stability of switched positive linear time‐delay systems. By developing a novel multiple discontinuous co‐positive Lyapunov–Krasovskii functional approach, the stability conditions are established for switched positive time delay systems by a linear programming approach under mode‐dependent average dwell time switching. Moreover, under average dwell time switching, the corresponding stability conditions are also proposed. It is shown that their results can obtain smaller lower bounds on dwell time. Finally, simulation results are given to show the effectiveness of their methods. [ABSTRACT FROM AUTHOR]

Abstract This study investigates finite-time stability and stabilization problems for positive systems with impulses. By constructing a time-varying copositive Lyapunov function and utilizing the average impulsive interval approach, the finite-time stability criterion is established for the first time by exposing different impulsive effects. The relationship between the impulses and the length of the finite time interval is revealed via both theoretical analysis and simulations. As an extension, the finite-time L 1 gain performance is also addressed. Based on the finite-time stability results, the finite-time controller design problem is studied to guarantee the positivity and finite-time stability of the corresponding closed-loop system. The obtained criteria can be checked by the linear programming method. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results. Highlights • Finite-time stability and stabilization problems for impulsive positive systems (IPSs) are solved firstly. • Relationship between impulses and length of finite time interval is revealed deeply. • A time-varying Lyapunov copositive function (LCF) and the average impulsive interval method are utilized. • All the proposed criteria can be checked by the linear programming approach. [ABSTRACT FROM AUTHOR]

In this paper, we study an optimization problem of minimizing a linear function subject to fuzzy relational inequalities with the addition–min composition. This optimization setting has recently been proposed to model the network cogestion issue when a BitTorrent-like peer-to-peer file-sharing system is used for data transmission. In a 2014 paper, a pseudominimal index (PMI)-based approach was proposed to search for an optimal solution. It turns out that the PMI-based approach may require to solve several to many linear programming problems in order to get an optimal solution. In this paper, we point out that the feasible domain is indeed convex. And we only need to solve a single linear programming problem to generate an optimal solution for the original optimization problem. Furthermore, our approach could be extended to the case with a nonlinear continuous objective function. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control. [ABSTRACT FROM AUTHOR]

The main results of the paper are concerned with determining the optimal stationary strategies for stochastic discrete control problems on networks with discounted costs. We ground polynomial time algorithms for determining the optimal strategies of this problem using a linear programming approach. Additionally, we show that the proposed approach can be extended for Markov decision processes with a total discounted cost optimization criterion. [ABSTRACT FROM AUTHOR]

This study investigates the feedback control for a class of switched positive linear systems (SPLSs). By means of the linear programming approach, output‐feedback and state‐feedback controllers for the underlying systems with average dwell time are designed, respectively. Under these controllers, the closed‐loop systems are positive and asymptotically stable. These results obtained provide a way to solve the control synthesis problems of SPLSs by multiple linear copositive Lyapunov functions. Finally, an example is given to illustrate the validity of the present design. [ABSTRACT FROM AUTHOR]

The topic of the paper is computer testing of (probabilistic) conditional independence (CI) implications by an algebraic method of structural imsets. The basic idea is to transform (sets of) CI statements into certain integral vectors and to verify by a computer the corresponding algebraic relation between the vectors, called the independence implication. We interpret the previous methods for computer testing of this implication from the point of view of polyhedral geometry. However, the main contribution of the paper is a new method, based on linear programming (LP). The new method overcomes the limitation of former methods to the number of involved variables. We recall/describe the theoretical basis for all four methods involved in our computational experiments, whose aim was to compare the efficiency of the algorithms. The experiments show that the LP method is clearly the fastest one. As an example of possible application of such algorithms we show that testing inclusion of Bayesian network structures or whether a CI statement is encoded in an acyclic directed graph can be done by the algebraic method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is two fold. First to establish the theory of discounted constrained Markov decision processes with a countable state and action spaces with general multi-chain structure. Second, to introduce finite approximation methods. We define the occupation measures and obtain properties of the set of all achievable occupation measures under the different admissible policies. We establish the optimality of stationary policies for the constrained control problem, and obtain an LP with a countable number of decision variables through which stationary optimal policies are computed. Since for such an LP one cannot expect to find an optimal solution in a finite number of operations, we present two schemes for finite approximations and establish the convergence of optimal values and policies for both the discounted and the expected average cost, with unbounded cost. Sometimes it turns out to be easier to solve the problem with infinite state space than the problem with finite yet large state space. Based on the optimal policy for the problem with infinite state space, we construct policies which are almost optimal for the problem with truncated state space. This method is applied to obtain an €-optimal policy for a problem of optimal priority assignment under constraints for a system of K finite queues. [ABSTRACT FROM AUTHOR]

The purpose of this study is to develop an automation platform that particularly emphases the beam reinforcements of a continuous beam of an RC building and automatically checks all designs to ensure that the arrangements of reinforcements comply with the American Concrete Institute code. The platform can establish the types of location patterns of lap splices (called lapping patterns) for the longitudinal reinforcements; calculate the length of every reinforcement; arrange the same sized reinforcements by length in decreasing order; choose the proper stock lengths for bar cutting; and determine the best lapping pattern with optimal stock length by the trial and error method or the linear programming approach, which can yield the most economical way to supply a proper stock length for cutting. Finally, the platform can automatically generate the shop drawing and schedule the reinforcements, which may be very useful for building construction and management. [ABSTRACT FROM AUTHOR]